反射三角形九点圆圆心

hbghlyj · 2023-3-15 04:55

Last edited by hbghlyj 2023-4-19 15:34$\triangle A'B'C'$是$\triangle ABC$关于平面上一点$P$的反射三角形.
过九点圆圆心$N$作$AA',BB',CC'$平行线,求证:这三条直线关于对应边反射后共点,这个点是$OP$中点,$O$为外心.

</td></tr></table>

</div>
<div id="comment_51648" class="cm">
</div>

</td></tr>
<tr><td class="plc plm">
</td>
</tr>
<tr id="_postposition51648"></tr>
<tr>
<td class="pls"></td>
<td class="plc" style="overflow:visible;">
<div class="po hin">
<div class="pob cl">
<em>
<a class="fastre" href="forum.php?mod=post&action=reply&fid=5&tid=10452&repquote=51648&extra=page%3D1&page=1" onclick="showWindow('reply', this.href)">Reply</a>
<a class="editp" href="forum.php?mod=post&action=edit&fid=5&tid=10452&pid=51648&page=1" onclick="showWindow('edit', this.href, 'get', 0)">Edit</a>
</em>

</div>
</div>
</td>
</tr>
<tr class="ad">
<td class="pls">
</td>
<td class="plc">
</td>
</tr>
</table>
<script type="text/javascript" reload="1">
aimgcount[51648] = ['13625'];
attachimggroup(51648);
attachimgshow(51648);
var aimgfid = 0;
</script>
</div><div id="post_51705" ><table id="pid51705" class="plhin" summary="pid51705" cellspacing="0" cellpadding="0">
<tr>
 <td class="pls" rowspan="2">
<div id="favatar51705" class="pls cl favatar">
<div class="pi">
<div class="authi"><a href="home.php?mod=space&uid=2719" target="_blank" class="xw1">TSC999</a>
</div>
</div>
<div class="p_pop blk bui card_gender_0" id="userinfo51705" style="display: none; margin-top: -11px;">
<div class="m z">
<div id="userinfo51705_ma"></div>
</div>
<div class="i y">
<div>
<strong><a href="home.php?mod=space&uid=2719" target="_blank" class="xi2">TSC999</a></strong>
<em>Offline</em>
</div><dl class="cl">
<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2719&do=profile" target="_blank" class="xi2">3152</a></dd>
</dl><div class="imicn">
<a href="home.php?mod=space&uid=2719&do=profile" target="_blank" title="View details"><img src="static/image/common/userinfo.gif" alt="View details" /></a>
</div>
<div id="avatarfeed"><span id="threadsortswait"></span></div>
</div>
</div>
<div>
</div>
<div class="tns xg2"><table cellspacing="0" cellpadding="0"><th><p><a href="home.php?mod=space&uid=2719&do=thread&type=thread&view=me&from=space" class="xi2">126</a></p>Threads</th><th><p><a href="home.php?mod=space&uid=2719&do=thread&type=reply&view=me&from=space" class="xi2">430</a></p>Posts</th><td><p><a href="home.php?mod=space&uid=2719&do=profile" class="xi2">3152</a></p>Credits</td></table></div>

<dl class="pil cl">
	<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2719&do=profile" target="_blank" class="xi2">3152</a></dd>
</dl>

<dl class="pil cl"></dl><p style="font-size: 12px;"><a href="thread-10452-1-1.html" rel="nofollow">Show all posts</a></p>
<ul class="xl xl2 o cl">
<li class="pm2"><a href="home.php?mod=spacecp&ac=pm&op=showmsg&handlekey=showmsg_2719&touid=2719&pmid=0&daterange=2&pid=51705&tid=10452" onclick="showWindow('sendpm', this.href);" title="Send PM" class="xi2">Send PM</a></li>
</ul>
</div>
</td>
<td class="plc">
<div class="pi">
<div class="pti">
<div class="pdbt">
</div>
<div class="authi">
<img class="authicn vm" id="authicon51705" src="static/image/common/online_member.svg" />
<a href="home.php?mod=space&uid=2719" target="_blank" class="xi2 neiid">TSC999</a>

Posted  <em id="authorposton51705">2023-3-16 13:16</em>
</div>
</div>
</div><div class="pct"><div class="pcb">
<div class="t_fsz"><table cellspacing="0" cellpadding="0"><tr><td class="t_f" id="postmessage_51705">
一条直线关于一个定点的反射线是咋定义的？<br />
一知直线关于另一条直线的反射线是咋定义的？</td></tr></table>

</div>
<div id="comment_51705" class="cm">
</div>

</td></tr>
<tr><td class="plc plm">
</td>
</tr>
<tr id="_postposition51705"></tr>
<tr>
<td class="pls"></td>
<td class="plc" style="overflow:visible;">
<div class="po hin">
<div class="pob cl">
<em>
<a class="fastre" href="forum.php?mod=post&action=reply&fid=5&tid=10452&repquote=51705&extra=page%3D1&page=1" onclick="showWindow('reply', this.href)">Reply</a>
<a class="editp" href="forum.php?mod=post&action=edit&fid=5&tid=10452&pid=51705&page=1" onclick="showWindow('edit', this.href, 'get', 0)">Edit</a>
<a class="replyadd"  onclick="showWindow('login','member.php?mod=logging&action=login')" title=""> <span id="review_support_51705"></span></a>
<a class="replysubtract"  onclick="showWindow('login','member.php?mod=logging&action=login')" onmouseover="this.title = ($('review_against_51705').innerHTML ? $('review_against_51705').innerHTML : 0) + ' users'"> <span id="review_against_51705"></span></a>
</em>

</div>
</div>
</td>
</tr>
<tr class="ad">
<td class="pls">
</td>
<td class="plc">
</td>
</tr>
</table>
</div><div id="post_51707" ><table id="pid51707" class="plhin" summary="pid51707" cellspacing="0" cellpadding="0">
<tr>
 <td class="pls" rowspan="2">
<div id="favatar51707" class="pls cl favatar">
<div class="pi">
<div class="authi"><a href="home.php?mod=space&uid=2861" target="_blank" class="xw1">hbghlyj</a>
</div>
</div>
<div class="p_pop blk bui card_gender_2" id="userinfo51707" style="display: none; margin-top: -11px;">
<div class="m z">
<div id="userinfo51707_ma"></div>
</div>
<div class="i y">
<div>
<strong><a href="home.php?mod=space&uid=2861" target="_blank" class="xi2">hbghlyj</a></strong>
<em>Offline</em>
</div><dl class="cl">
<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl><div class="imicn">
<a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="QQ"><img src="static/image/common/qq.gif" alt="QQ" /></a><a href="javascript:;" onclick="window.open('//amos.im.alisoft.com/msg.aw?v=2&uid='+encodeURIComponent('阿里旺旺')+'&site=cntaobao&s=2&charset=utf-8')" title="Wangwang"><img src="static/image/common/taobao.gif" alt="Wangwang" /></a><a href="https://cjhb.site" target="_blank" title="'s Homepage"><img src="static/image/common/forumlink.gif" alt="'s Homepage" /></a><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" title="View details"><img src="static/image/common/userinfo.gif" alt="View details" /></a>
</div>
<div id="avatarfeed"><span id="threadsortswait"></span></div>
</div>
</div>
<div>
<div class="avatar"><a href="home.php?mod=space&uid=2861" class="avtm" target="_blank"><img src="./data/avatar/000/00/28/61_avatar_middle.jpg" class="user_avatar"></a></div>
</div>
<div class="tns xg2"><table cellspacing="0" cellpadding="0"><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=thread&view=me&from=space" class="xi2">3159</a></p>Threads</th><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=reply&view=me&from=space" class="xi2">7941</a></p>Posts</th><td><p><a href="home.php?mod=space&uid=2861&do=profile" class="xi2"><span title="63770">610K</span></a></p>Credits</td></table></div>

<dl class="pil cl">
	<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl>

<dl class="pil cl"><a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="Start QQ chat"><img src="static/image/common/qq_big.gif" alt="QQ" style="margin:0px;"/></a></dl><p style="font-size: 12px;"><a href="thread-10452-1-1.html" rel="nofollow">Show all posts</a></p>
<ul class="xl xl2 o cl">
<li class="pm2"><a href="home.php?mod=spacecp&ac=pm&op=showmsg&handlekey=showmsg_2861&touid=2861&pmid=0&daterange=2&pid=51707&tid=10452" onclick="showWindow('sendpm', this.href);" title="Send PM" class="xi2">Send PM</a></li>
</ul>
</div>
</td>
<td class="plc">
<div class="pi">
<div class="pti">
<div class="pdbt">
</div>
<div class="authi">
<em class="authicn fico-person fic4 fnmr vm" id="authicon51707" title="Author"></em>
 Author<span class="pipe">|</span>
<a href="home.php?mod=space&uid=2861" target="_blank" class="xi2 neiid">hbghlyj</a>

Posted  <em id="authorposton51707">2023-3-16 16:12</em>
</div>
</div>
</div><div class="pct"><div class="pcb">
<div class="t_fsz"><table cellspacing="0" cellpadding="0"><tr><td class="t_f" id="postmessage_51707">
<div class="quote"><blockquote><font size="2"><a href="forum.php?mod=redirect&goto=findpost&pid=51705&ptid=10452" target="_blank"><font color="#999">TSC999 发表于 2023-3-16 06:16</font></a></font><br />
一条直线关于一个定点的反射线是咋定义的？<br />
一知直线关于另一条直线的反射线是咋定义的？ ...</blockquote></div>就是點對稱 Geogebra有工具<br />
<a href="https://wiki.geogebra.org/zh/%E9%BB%9E%E5%B0%8D%E7%A8%B1_%E5%B7%A5%E5%85%B7" target="_blank">wiki.geogebra.org/zh/點對稱_工具</a><br />
<br />
选择要反射的对象。 然后，单击一个点以指定反射中心。
<ignore_js_op>

</ignore_js_op>
<br />
<br />
<a href="https://wiki.geogebra.org/en/Reflect_Command" target="_blank">wiki.geogebra.org/en/Reflect_Command</a><br />
<br />
反射（<对象>，<点>）<br />
     关于给定点反射几何对象。<br />
 <br />
 反射（<对象>，<线>）<br />
     关于给定的线反射一个对象。<br />
<br />
 反射（<对象>，<圆>）<br />
     相对于圆反演几何对象。<br />
<br />
 反射（<对象>，<平面>）<br />
     关于平面反射对象。</td></tr></table>

</div>
<div id="comment_51707" class="cm">
</div>

</td></tr>
<tr><td class="plc plm">
</td>
</tr>
<tr id="_postposition51707"></tr>
<tr>
<td class="pls"></td>
<td class="plc" style="overflow:visible;">
<div class="po hin">
<div class="pob cl">
<em>
<a class="fastre" href="forum.php?mod=post&action=reply&fid=5&tid=10452&repquote=51707&extra=page%3D1&page=1" onclick="showWindow('reply', this.href)">Reply</a>
<a class="editp" href="forum.php?mod=post&action=edit&fid=5&tid=10452&pid=51707&page=1" onclick="showWindow('edit', this.href, 'get', 0)">Edit</a>
<a class="replyadd"  onclick="showWindow('login','member.php?mod=logging&action=login')" title=""> <span id="review_support_51707"></span></a>
<a class="replysubtract"  onclick="showWindow('login','member.php?mod=logging&action=login')" onmouseover="this.title = ($('review_against_51707').innerHTML ? $('review_against_51707').innerHTML : 0) + ' users'"> <span id="review_against_51707"></span></a>
</em>

</div>
</div>
</td>
</tr>
<tr class="ad">
<td class="pls">
</td>
<td class="plc">
</td>
</tr>
</table>
<script type="text/javascript" reload="1">
aimgcount[51707] = ['13638'];
attachimggroup(51707);
attachimgshow(51707);
var aimgfid = 0;
</script>
</div><div id="post_51769" ><table id="pid51769" class="plhin" summary="pid51769" cellspacing="0" cellpadding="0">
<tr>
 <td class="pls" rowspan="2">
<div id="favatar51769" class="pls cl favatar">
<div class="pi">
<div class="authi"><a href="home.php?mod=space&uid=2719" target="_blank" class="xw1">TSC999</a>
</div>
</div>
<div class="p_pop blk bui card_gender_0" id="userinfo51769" style="display: none; margin-top: -11px;">
<div class="m z">
<div id="userinfo51769_ma"></div>
</div>
<div class="i y">
<div>
<strong><a href="home.php?mod=space&uid=2719" target="_blank" class="xi2">TSC999</a></strong>
<em>Offline</em>
</div><dl class="cl">
<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2719&do=profile" target="_blank" class="xi2">3152</a></dd>
</dl><div class="imicn">
<a href="home.php?mod=space&uid=2719&do=profile" target="_blank" title="View details"><img src="static/image/common/userinfo.gif" alt="View details" /></a>
</div>
<div id="avatarfeed"><span id="threadsortswait"></span></div>
</div>
</div>
<div>
</div>
<div class="tns xg2"><table cellspacing="0" cellpadding="0"><th><p><a href="home.php?mod=space&uid=2719&do=thread&type=thread&view=me&from=space" class="xi2">126</a></p>Threads</th><th><p><a href="home.php?mod=space&uid=2719&do=thread&type=reply&view=me&from=space" class="xi2">430</a></p>Posts</th><td><p><a href="home.php?mod=space&uid=2719&do=profile" class="xi2">3152</a></p>Credits</td></table></div>

<dl class="pil cl">
	<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2719&do=profile" target="_blank" class="xi2">3152</a></dd>
</dl>

<dl class="pil cl"></dl><p style="font-size: 12px;"><a href="thread-10452-1-1.html" rel="nofollow">Show all posts</a></p>
<ul class="xl xl2 o cl">
<li class="pm2"><a href="home.php?mod=spacecp&ac=pm&op=showmsg&handlekey=showmsg_2719&touid=2719&pmid=0&daterange=2&pid=51769&tid=10452" onclick="showWindow('sendpm', this.href);" title="Send PM" class="xi2">Send PM</a></li>
</ul>
</div>
</td>
<td class="plc">
<div class="pi">
<div class="pti">
<div class="pdbt">
</div>
<div class="authi">
<img class="authicn vm" id="authicon51769" src="static/image/common/online_member.svg" />
<a href="home.php?mod=space&uid=2719" target="_blank" class="xi2 neiid">TSC999</a>

Posted  <em id="authorposton51769">2023-3-17 17:27</em>
</div>
</div>
</div><div class="pct"><div class="pcb">
<div class="t_fsz"><table cellspacing="0" cellpadding="0"><tr><td class="t_f" id="postmessage_51769">
给定直线 AB 和定点 P，如何人工作出 AB 关于 P 点的反射线 $A'B'$？<br />

<ignore_js_op>

</ignore_js_op>
</td></tr></table>

</div>
<div id="comment_51769" class="cm">
</div>

</td></tr>
<tr><td class="plc plm">
</td>
</tr>
<tr id="_postposition51769"></tr>
<tr>
<td class="pls"></td>
<td class="plc" style="overflow:visible;">
<div class="po hin">
<div class="pob cl">
<em>
<a class="fastre" href="forum.php?mod=post&action=reply&fid=5&tid=10452&repquote=51769&extra=page%3D1&page=1" onclick="showWindow('reply', this.href)">Reply</a>
<a class="editp" href="forum.php?mod=post&action=edit&fid=5&tid=10452&pid=51769&page=1" onclick="showWindow('edit', this.href, 'get', 0)">Edit</a>
<a class="replyadd"  onclick="showWindow('login','member.php?mod=logging&action=login')" title=""> <span id="review_support_51769"></span></a>
<a class="replysubtract"  onclick="showWindow('login','member.php?mod=logging&action=login')" onmouseover="this.title = ($('review_against_51769').innerHTML ? $('review_against_51769').innerHTML : 0) + ' users'"> <span id="review_against_51769"></span></a>
</em>

</div>
</div>
</td>
</tr>
<tr class="ad">
<td class="pls">
</td>
<td class="plc">
</td>
</tr>
</table>
<script type="text/javascript" reload="1">
aimgcount[51769] = ['13658'];
attachimggroup(51769);
attachimgshow(51769);
var aimgfid = 0;
</script>
</div><div id="post_51770" ><table id="pid51770" class="plhin" summary="pid51770" cellspacing="0" cellpadding="0">
<tr>
 <td class="pls" rowspan="2">
<div id="favatar51770" class="pls cl favatar">
<div class="pi">
<div class="authi"><a href="home.php?mod=space&uid=2861" target="_blank" class="xw1">hbghlyj</a>
</div>
</div>
<div class="p_pop blk bui card_gender_2" id="userinfo51770" style="display: none; margin-top: -11px;">
<div class="m z">
<div id="userinfo51770_ma"></div>
</div>
<div class="i y">
<div>
<strong><a href="home.php?mod=space&uid=2861" target="_blank" class="xi2">hbghlyj</a></strong>
<em>Offline</em>
</div><dl class="cl">
<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl><div class="imicn">
<a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="QQ"><img src="static/image/common/qq.gif" alt="QQ" /></a><a href="javascript:;" onclick="window.open('//amos.im.alisoft.com/msg.aw?v=2&uid='+encodeURIComponent('阿里旺旺')+'&site=cntaobao&s=2&charset=utf-8')" title="Wangwang"><img src="static/image/common/taobao.gif" alt="Wangwang" /></a><a href="https://cjhb.site" target="_blank" title="'s Homepage"><img src="static/image/common/forumlink.gif" alt="'s Homepage" /></a><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" title="View details"><img src="static/image/common/userinfo.gif" alt="View details" /></a>
</div>
<div id="avatarfeed"><span id="threadsortswait"></span></div>
</div>
</div>
<div>
<div class="avatar"><a href="home.php?mod=space&uid=2861" class="avtm" target="_blank"><img src="./data/avatar/000/00/28/61_avatar_middle.jpg" class="user_avatar"></a></div>
</div>
<div class="tns xg2"><table cellspacing="0" cellpadding="0"><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=thread&view=me&from=space" class="xi2">3159</a></p>Threads</th><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=reply&view=me&from=space" class="xi2">7941</a></p>Posts</th><td><p><a href="home.php?mod=space&uid=2861&do=profile" class="xi2"><span title="63770">610K</span></a></p>Credits</td></table></div>

<dl class="pil cl">
	<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl>

<dl class="pil cl"><a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="Start QQ chat"><img src="static/image/common/qq_big.gif" alt="QQ" style="margin:0px;"/></a></dl><p style="font-size: 12px;"><a href="thread-10452-1-1.html" rel="nofollow">Show all posts</a></p>
<ul class="xl xl2 o cl">
<li class="pm2"><a href="home.php?mod=spacecp&ac=pm&op=showmsg&handlekey=showmsg_2861&touid=2861&pmid=0&daterange=2&pid=51770&tid=10452" onclick="showWindow('sendpm', this.href);" title="Send PM" class="xi2">Send PM</a></li>
</ul>
</div>
</td>
<td class="plc">
<div class="pi">
<div class="pti">
<div class="pdbt">
</div>
<div class="authi">
<em class="authicn fico-person fic4 fnmr vm" id="authicon51770" title="Author"></em>
 Author<span class="pipe">|</span>
<a href="home.php?mod=space&uid=2861" target="_blank" class="xi2 neiid">hbghlyj</a>

Posted  <em id="authorposton51770">2023-3-17 17:29</em>
</div>
</div>
</div><div class="pct"><div class="pcb">
<div class="t_fsz"><table cellspacing="0" cellpadding="0"><tr><td class="t_f" id="postmessage_51770">
<div class="quote"><blockquote><font size="2"><a href="forum.php?mod=redirect&goto=findpost&pid=51769&ptid=10452" target="_blank"><font color="#999">TSC999 发表于 2023-3-17 10:27</font></a></font><br />
给定直线 AB 和定点 P，如何人工作出 AB 关于 P 点的反射线？</blockquote></div>图中标的$A',B'$都不是 AB 关于 P 点的反射啊<img src="static/image/smiley/default/shocked.gif" smilieid="6" border="0" alt="" /></td></tr></table>

</div>
<div id="comment_51770" class="cm">
<h3 class="psth xs1"><span class="icon_ring vm"></span>Comment</h3>
<div class="pstl xs1 cl">
<div class="psta vm">
<a href="home.php?mod=space&uid=2719" c="1"><img src="./data/avatar/noavatar.svg" class="user_avatar"></a>
<a href="home.php?mod=space&uid=2719" class="xi2 xw1">TSC999</a>
</div>
<div class="psti">如何人工作出来？不要用Geogebra 软件作。 
<span class="xg1">
Posted  2023-3-17 17:32</span>
</div>
</div>
</div>

</td></tr>
<tr><td class="plc plm">
</td>
</tr>
<tr id="_postposition51770"></tr>
<tr>
<td class="pls"></td>
<td class="plc" style="overflow:visible;">
<div class="po hin">
<div class="pob cl">
<em>
<a class="fastre" href="forum.php?mod=post&action=reply&fid=5&tid=10452&repquote=51770&extra=page%3D1&page=1" onclick="showWindow('reply', this.href)">Reply</a>
<a class="editp" href="forum.php?mod=post&action=edit&fid=5&tid=10452&pid=51770&page=1" onclick="showWindow('edit', this.href, 'get', 0)">Edit</a>
<a class="replyadd"  onclick="showWindow('login','member.php?mod=logging&action=login')" title=""> <span id="review_support_51770"></span></a>
<a class="replysubtract"  onclick="showWindow('login','member.php?mod=logging&action=login')" onmouseover="this.title = ($('review_against_51770').innerHTML ? $('review_against_51770').innerHTML : 0) + ' users'"> <span id="review_against_51770"></span></a>
</em>

</div>
</div>
</td>
</tr>
<tr class="ad">
<td class="pls">
</td>
<td class="plc">
</td>
</tr>
</table>
</div><div id="post_51772" ><table id="pid51772" class="plhin" summary="pid51772" cellspacing="0" cellpadding="0">
<tr>
 <td class="pls" rowspan="2">
<div id="favatar51772" class="pls cl favatar">
<div class="pi">
<div class="authi"><a href="home.php?mod=space&uid=2719" target="_blank" class="xw1">TSC999</a>
</div>
</div>
<div class="p_pop blk bui card_gender_0" id="userinfo51772" style="display: none; margin-top: -11px;">
<div class="m z">
<div id="userinfo51772_ma"></div>
</div>
<div class="i y">
<div>
<strong><a href="home.php?mod=space&uid=2719" target="_blank" class="xi2">TSC999</a></strong>
<em>Offline</em>
</div><dl class="cl">
<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2719&do=profile" target="_blank" class="xi2">3152</a></dd>
</dl><div class="imicn">
<a href="home.php?mod=space&uid=2719&do=profile" target="_blank" title="View details"><img src="static/image/common/userinfo.gif" alt="View details" /></a>
</div>
<div id="avatarfeed"><span id="threadsortswait"></span></div>
</div>
</div>
<div>
</div>
<div class="tns xg2"><table cellspacing="0" cellpadding="0"><th><p><a href="home.php?mod=space&uid=2719&do=thread&type=thread&view=me&from=space" class="xi2">126</a></p>Threads</th><th><p><a href="home.php?mod=space&uid=2719&do=thread&type=reply&view=me&from=space" class="xi2">430</a></p>Posts</th><td><p><a href="home.php?mod=space&uid=2719&do=profile" class="xi2">3152</a></p>Credits</td></table></div>

<dl class="pil cl">
	<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2719&do=profile" target="_blank" class="xi2">3152</a></dd>
</dl>

<dl class="pil cl"></dl><p style="font-size: 12px;"><a href="thread-10452-1-1.html" rel="nofollow">Show all posts</a></p>
<ul class="xl xl2 o cl">
<li class="pm2"><a href="home.php?mod=spacecp&ac=pm&op=showmsg&handlekey=showmsg_2719&touid=2719&pmid=0&daterange=2&pid=51772&tid=10452" onclick="showWindow('sendpm', this.href);" title="Send PM" class="xi2">Send PM</a></li>
</ul>
</div>
</td>
<td class="plc">
<div class="pi">
<div class="pti">
<div class="pdbt">
</div>
<div class="authi">
<img class="authicn vm" id="authicon51772" src="static/image/common/online_member.svg" />
<a href="home.php?mod=space&uid=2719" target="_blank" class="xi2 neiid">TSC999</a>

Posted  <em id="authorposton51772">2023-3-17 17:33</em>
</div>
</div>
</div><div class="pct"><div class="pcb">
<div class="t_fsz"><table cellspacing="0" cellpadding="0"><tr><td class="t_f" id="postmessage_51772">
<div class="quote"><blockquote><font size="2"><a href="forum.php?mod=redirect&goto=findpost&pid=51770&ptid=10452" target="_blank"><font color="#999">hbghlyj 发表于 2023-3-17 17:29</font></a></font><br />
图中标的$A',B'$都不是 AB 关于 P 点的反射啊</blockquote></div> 如何人工作出来？不要用Geogebra 软件作。</td></tr></table>

</div>
<div id="comment_51772" class="cm">
</div>

</td></tr>
<tr><td class="plc plm">
</td>
</tr>
<tr id="_postposition51772"></tr>
<tr>
<td class="pls"></td>
<td class="plc" style="overflow:visible;">
<div class="po hin">
<div class="pob cl">
<em>
<a class="fastre" href="forum.php?mod=post&action=reply&fid=5&tid=10452&repquote=51772&extra=page%3D1&page=1" onclick="showWindow('reply', this.href)">Reply</a>
<a class="editp" href="forum.php?mod=post&action=edit&fid=5&tid=10452&pid=51772&page=1" onclick="showWindow('edit', this.href, 'get', 0)">Edit</a>
<a class="replyadd"  onclick="showWindow('login','member.php?mod=logging&action=login')" title=""> <span id="review_support_51772"></span></a>
<a class="replysubtract"  onclick="showWindow('login','member.php?mod=logging&action=login')" onmouseover="this.title = ($('review_against_51772').innerHTML ? $('review_against_51772').innerHTML : 0) + ' users'"> <span id="review_against_51772"></span></a>
</em>

</div>
</div>
</td>
</tr>
<tr class="ad">
<td class="pls">
</td>
<td class="plc">
</td>
</tr>
</table>
</div><div id="post_51773" ><table id="pid51773" class="plhin" summary="pid51773" cellspacing="0" cellpadding="0">
<tr>
 <td class="pls" rowspan="2">
<div id="favatar51773" class="pls cl favatar">
<div class="pi">
<div class="authi"><a href="home.php?mod=space&uid=2861" target="_blank" class="xw1">hbghlyj</a>
</div>
</div>
<div class="p_pop blk bui card_gender_2" id="userinfo51773" style="display: none; margin-top: -11px;">
<div class="m z">
<div id="userinfo51773_ma"></div>
</div>
<div class="i y">
<div>
<strong><a href="home.php?mod=space&uid=2861" target="_blank" class="xi2">hbghlyj</a></strong>
<em>Offline</em>
</div><dl class="cl">
<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl><div class="imicn">
<a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="QQ"><img src="static/image/common/qq.gif" alt="QQ" /></a><a href="javascript:;" onclick="window.open('//amos.im.alisoft.com/msg.aw?v=2&uid='+encodeURIComponent('阿里旺旺')+'&site=cntaobao&s=2&charset=utf-8')" title="Wangwang"><img src="static/image/common/taobao.gif" alt="Wangwang" /></a><a href="https://cjhb.site" target="_blank" title="'s Homepage"><img src="static/image/common/forumlink.gif" alt="'s Homepage" /></a><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" title="View details"><img src="static/image/common/userinfo.gif" alt="View details" /></a>
</div>
<div id="avatarfeed"><span id="threadsortswait"></span></div>
</div>
</div>
<div>
<div class="avatar"><a href="home.php?mod=space&uid=2861" class="avtm" target="_blank"><img src="./data/avatar/000/00/28/61_avatar_middle.jpg" class="user_avatar"></a></div>
</div>
<div class="tns xg2"><table cellspacing="0" cellpadding="0"><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=thread&view=me&from=space" class="xi2">3159</a></p>Threads</th><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=reply&view=me&from=space" class="xi2">7941</a></p>Posts</th><td><p><a href="home.php?mod=space&uid=2861&do=profile" class="xi2"><span title="63770">610K</span></a></p>Credits</td></table></div>

<dl class="pil cl">
	<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl>

<dl class="pil cl"><a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="Start QQ chat"><img src="static/image/common/qq_big.gif" alt="QQ" style="margin:0px;"/></a></dl><p style="font-size: 12px;"><a href="thread-10452-1-1.html" rel="nofollow">Show all posts</a></p>
<ul class="xl xl2 o cl">
<li class="pm2"><a href="home.php?mod=spacecp&ac=pm&op=showmsg&handlekey=showmsg_2861&touid=2861&pmid=0&daterange=2&pid=51773&tid=10452" onclick="showWindow('sendpm', this.href);" title="Send PM" class="xi2">Send PM</a></li>
</ul>
</div>
</td>
<td class="plc">
<div class="pi">
<div class="pti">
<div class="pdbt">
</div>
<div class="authi">
<em class="authicn fico-person fic4 fnmr vm" id="authicon51773" title="Author"></em>
 Author<span class="pipe">|</span>
<a href="home.php?mod=space&uid=2861" target="_blank" class="xi2 neiid">hbghlyj</a>

Posted  <em id="authorposton51773">2023-3-17 17:33</em>
</div>
</div>
</div><div class="pct"><div class="pcb">
<div class="t_fsz"><table cellspacing="0" cellpadding="0"><tr><td class="t_f" id="postmessage_51773">
<div class="quote"><blockquote><font size="2"><a href="forum.php?mod=redirect&goto=findpost&pid=51769&ptid=10452" target="_blank"><font color="#999">TSC999 发表于 2023-3-17 10:27</font></a></font><br />
给定直线 AB 和定点 P，如何人工作出 AB 关于 P 点的反射线 $A'B'$？</blockquote></div>只要延长$AP$到$A'$使$AP=A'P$即可</td></tr></table>

</div>
<div id="comment_51773" class="cm">
</div>

</td></tr>
<tr><td class="plc plm">
</td>
</tr>
<tr id="_postposition51773"></tr>
<tr>
<td class="pls"></td>
<td class="plc" style="overflow:visible;">
<div class="po hin">
<div class="pob cl">
<em>
<a class="fastre" href="forum.php?mod=post&action=reply&fid=5&tid=10452&repquote=51773&extra=page%3D1&page=1" onclick="showWindow('reply', this.href)">Reply</a>
<a class="editp" href="forum.php?mod=post&action=edit&fid=5&tid=10452&pid=51773&page=1" onclick="showWindow('edit', this.href, 'get', 0)">Edit</a>
<a class="replyadd"  onclick="showWindow('login','member.php?mod=logging&action=login')" title=""> <span id="review_support_51773"></span></a>
<a class="replysubtract"  onclick="showWindow('login','member.php?mod=logging&action=login')" onmouseover="this.title = ($('review_against_51773').innerHTML ? $('review_against_51773').innerHTML : 0) + ' users'"> <span id="review_against_51773"></span></a>
</em>

</div>
</div>
</td>
</tr>
<tr class="ad">
<td class="pls">
</td>
<td class="plc">
</td>
</tr>
</table>
</div><div id="post_51774" ><table id="pid51774" class="plhin" summary="pid51774" cellspacing="0" cellpadding="0">
<tr>
 <td class="pls" rowspan="2">
<div id="favatar51774" class="pls cl favatar">
<div class="pi">
<div class="authi"><a href="home.php?mod=space&uid=2861" target="_blank" class="xw1">hbghlyj</a>
</div>
</div>
<div class="p_pop blk bui card_gender_2" id="userinfo51774" style="display: none; margin-top: -11px;">
<div class="m z">
<div id="userinfo51774_ma"></div>
</div>
<div class="i y">
<div>
<strong><a href="home.php?mod=space&uid=2861" target="_blank" class="xi2">hbghlyj</a></strong>
<em>Offline</em>
</div><dl class="cl">
<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl><div class="imicn">
<a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="QQ"><img src="static/image/common/qq.gif" alt="QQ" /></a><a href="javascript:;" onclick="window.open('//amos.im.alisoft.com/msg.aw?v=2&uid='+encodeURIComponent('阿里旺旺')+'&site=cntaobao&s=2&charset=utf-8')" title="Wangwang"><img src="static/image/common/taobao.gif" alt="Wangwang" /></a><a href="https://cjhb.site" target="_blank" title="'s Homepage"><img src="static/image/common/forumlink.gif" alt="'s Homepage" /></a><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" title="View details"><img src="static/image/common/userinfo.gif" alt="View details" /></a>
</div>
<div id="avatarfeed"><span id="threadsortswait"></span></div>
</div>
</div>
<div>
<div class="avatar"><a href="home.php?mod=space&uid=2861" class="avtm" target="_blank"><img src="./data/avatar/000/00/28/61_avatar_middle.jpg" class="user_avatar"></a></div>
</div>
<div class="tns xg2"><table cellspacing="0" cellpadding="0"><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=thread&view=me&from=space" class="xi2">3159</a></p>Threads</th><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=reply&view=me&from=space" class="xi2">7941</a></p>Posts</th><td><p><a href="home.php?mod=space&uid=2861&do=profile" class="xi2"><span title="63770">610K</span></a></p>Credits</td></table></div>

<dl class="pil cl">
	<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl>

<dl class="pil cl"><a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="Start QQ chat"><img src="static/image/common/qq_big.gif" alt="QQ" style="margin:0px;"/></a></dl><p style="font-size: 12px;"><a href="thread-10452-1-1.html" rel="nofollow">Show all posts</a></p>
<ul class="xl xl2 o cl">
<li class="pm2"><a href="home.php?mod=spacecp&ac=pm&op=showmsg&handlekey=showmsg_2861&touid=2861&pmid=0&daterange=2&pid=51774&tid=10452" onclick="showWindow('sendpm', this.href);" title="Send PM" class="xi2">Send PM</a></li>
</ul>
</div>
</td>
<td class="plc">
<div class="pi">
<div class="pti">
<div class="pdbt">
</div>
<div class="authi">
<em class="authicn fico-person fic4 fnmr vm" id="authicon51774" title="Author"></em>
 Author<span class="pipe">|</span>
<a href="home.php?mod=space&uid=2861" target="_blank" class="xi2 neiid">hbghlyj</a>

Posted  <em id="authorposton51774">2023-3-17 17:36</em>
</div>
</div>
</div><div class="pct"><div class="pcb">
<div class="t_fsz"><table cellspacing="0" cellpadding="0"><tr><td class="t_f" id="postmessage_51774">
<div class="quote"><blockquote><font size="2"><a href="forum.php?mod=redirect&goto=findpost&pid=51769&ptid=10452" target="_blank"><font color="#999">TSC999 发表于 2023-3-17 10:27</font></a></font><br />
给定直线 AB 和定点 P，如何人工作出 AB 关于 P 点的反射线 $A'B'$？</blockquote></div>這裡的 “反射線” 是指 點對稱 吧<br />

<ignore_js_op>

</ignore_js_op>
</td></tr></table>

</div>
<div id="comment_51774" class="cm">
<h3 class="psth xs1"><span class="icon_ring vm"></span>Comment</h3>
<div class="pstl xs1 cl">
<div class="psta vm">
<a href="home.php?mod=space&uid=2719" c="1"><img src="./data/avatar/noavatar.svg" class="user_avatar"></a>
<a href="home.php?mod=space&uid=2719" class="xi2 xw1">TSC999</a>
</div>
<div class="psti">这样作就不是那个图了。 
<span class="xg1">
Posted  2023-3-17 17:44</span>
</div>
</div>
</div>

</td></tr>
<tr><td class="plc plm">
</td>
</tr>
<tr id="_postposition51774"></tr>
<tr>
<td class="pls"></td>
<td class="plc" style="overflow:visible;">
<div class="po hin">
<div class="pob cl">
<em>
<a class="fastre" href="forum.php?mod=post&action=reply&fid=5&tid=10452&repquote=51774&extra=page%3D1&page=1" onclick="showWindow('reply', this.href)">Reply</a>
<a class="editp" href="forum.php?mod=post&action=edit&fid=5&tid=10452&pid=51774&page=1" onclick="showWindow('edit', this.href, 'get', 0)">Edit</a>
<a class="replyadd"  onclick="showWindow('login','member.php?mod=logging&action=login')" title=""> <span id="review_support_51774"></span></a>
<a class="replysubtract"  onclick="showWindow('login','member.php?mod=logging&action=login')" onmouseover="this.title = ($('review_against_51774').innerHTML ? $('review_against_51774').innerHTML : 0) + ' users'"> <span id="review_against_51774"></span></a>
</em>

</div>
</div>
</td>
</tr>
<tr class="ad">
<td class="pls">
</td>
<td class="plc">
</td>
</tr>
</table>
<script type="text/javascript" reload="1">
aimgcount[51774] = ['13659'];
attachimggroup(51774);
attachimgshow(51774);
var aimgfid = 0;
</script>
</div><div id="post_51777" ><table id="pid51777" class="plhin" summary="pid51777" cellspacing="0" cellpadding="0">
<tr>
 <td class="pls" rowspan="2">
<div id="favatar51777" class="pls cl favatar">
<div class="pi">
<div class="authi"><a href="home.php?mod=space&uid=2861" target="_blank" class="xw1">hbghlyj</a>
</div>
</div>
<div class="p_pop blk bui card_gender_2" id="userinfo51777" style="display: none; margin-top: -11px;">
<div class="m z">
<div id="userinfo51777_ma"></div>
</div>
<div class="i y">
<div>
<strong><a href="home.php?mod=space&uid=2861" target="_blank" class="xi2">hbghlyj</a></strong>
<em>Offline</em>
</div><dl class="cl">
<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl><div class="imicn">
<a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="QQ"><img src="static/image/common/qq.gif" alt="QQ" /></a><a href="javascript:;" onclick="window.open('//amos.im.alisoft.com/msg.aw?v=2&uid='+encodeURIComponent('阿里旺旺')+'&site=cntaobao&s=2&charset=utf-8')" title="Wangwang"><img src="static/image/common/taobao.gif" alt="Wangwang" /></a><a href="https://cjhb.site" target="_blank" title="'s Homepage"><img src="static/image/common/forumlink.gif" alt="'s Homepage" /></a><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" title="View details"><img src="static/image/common/userinfo.gif" alt="View details" /></a>
</div>
<div id="avatarfeed"><span id="threadsortswait"></span></div>
</div>
</div>
<div>
<div class="avatar"><a href="home.php?mod=space&uid=2861" class="avtm" target="_blank"><img src="./data/avatar/000/00/28/61_avatar_middle.jpg" class="user_avatar"></a></div>
</div>
<div class="tns xg2"><table cellspacing="0" cellpadding="0"><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=thread&view=me&from=space" class="xi2">3159</a></p>Threads</th><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=reply&view=me&from=space" class="xi2">7941</a></p>Posts</th><td><p><a href="home.php?mod=space&uid=2861&do=profile" class="xi2"><span title="63770">610K</span></a></p>Credits</td></table></div>

<dl class="pil cl">
	<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl>

<dl class="pil cl"><a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="Start QQ chat"><img src="static/image/common/qq_big.gif" alt="QQ" style="margin:0px;"/></a></dl><p style="font-size: 12px;"><a href="thread-10452-1-1.html" rel="nofollow">Show all posts</a></p>
<ul class="xl xl2 o cl">
<li class="pm2"><a href="home.php?mod=spacecp&ac=pm&op=showmsg&handlekey=showmsg_2861&touid=2861&pmid=0&daterange=2&pid=51777&tid=10452" onclick="showWindow('sendpm', this.href);" title="Send PM" class="xi2">Send PM</a></li>
</ul>
</div>
</td>
<td class="plc">
<div class="pi">
<div class="pti">
<div class="pdbt">
</div>
<div class="authi">
<em class="authicn fico-person fic4 fnmr vm" id="authicon51777" title="Author"></em>
 Author<span class="pipe">|</span>
<a href="home.php?mod=space&uid=2861" target="_blank" class="xi2 neiid">hbghlyj</a>

Posted  <em id="authorposton51777">2023-3-17 17:50</em>
</div>
</div>
</div><div class="pct"><div class="pcb">
<div class="t_fsz"><table cellspacing="0" cellpadding="0"><tr><td class="t_f" id="postmessage_51777">
<div class="quote"><blockquote><font size="2"><a href="forum.php?mod=redirect&goto=findpost&pid=51774&ptid=10452" target="_blank"><font color="#999">TSC999 发表于 2023-3-17 10:44</font></a></font><br />
这样作就不是那个图了。</blockquote></div>哪个图<img src="static/image/smiley/default/shocked.gif" smilieid="6" border="0" alt="" /></td></tr></table>

</div>
<div id="comment_51777" class="cm">
<h3 class="psth xs1"><span class="icon_ring vm"></span>Comment</h3>
<div class="pstl xs1 cl">
<div class="psta vm">
<a href="home.php?mod=space&uid=2719" c="1"><img src="./data/avatar/noavatar.svg" class="user_avatar"></a>
<a href="home.php?mod=space&uid=2719" class="xi2 xw1">TSC999</a>
</div>
<div class="psti">4# 楼的图。 
<span class="xg1">
Posted  2023-3-18 08:50</span>
</div>
</div>
</div>

</td></tr>
<tr><td class="plc plm">
</td>
</tr>
<tr id="_postposition51777"></tr>
<tr>
<td class="pls"></td>
<td class="plc" style="overflow:visible;">
<div class="po hin">
<div class="pob cl">
<em>
<a class="fastre" href="forum.php?mod=post&action=reply&fid=5&tid=10452&repquote=51777&extra=page%3D1&page=1" onclick="showWindow('reply', this.href)">Reply</a>
<a class="editp" href="forum.php?mod=post&action=edit&fid=5&tid=10452&pid=51777&page=1" onclick="showWindow('edit', this.href, 'get', 0)">Edit</a>
<a class="replyadd"  onclick="showWindow('login','member.php?mod=logging&action=login')" title=""> <span id="review_support_51777"></span></a>
<a class="replysubtract"  onclick="showWindow('login','member.php?mod=logging&action=login')" onmouseover="this.title = ($('review_against_51777').innerHTML ? $('review_against_51777').innerHTML : 0) + ' users'"> <span id="review_against_51777"></span></a>
</em>

</div>
</div>
</td>
</tr>
<tr class="ad">
<td class="pls">
</td>
<td class="plc">
</td>
</tr>
</table>
</div><div id="post_51816" ><table id="pid51816" class="plhin" summary="pid51816" cellspacing="0" cellpadding="0">
<tr>
 <td class="pls" rowspan="2">
<div id="favatar51816" class="pls cl favatar">
<div class="pi">
<div class="authi"><a href="home.php?mod=space&uid=2861" target="_blank" class="xw1">hbghlyj</a>
</div>
</div>
<div class="p_pop blk bui card_gender_2" id="userinfo51816" style="display: none; margin-top: -11px;">
<div class="m z">
<div id="userinfo51816_ma"></div>
</div>
<div class="i y">
<div>
<strong><a href="home.php?mod=space&uid=2861" target="_blank" class="xi2">hbghlyj</a></strong>
<em>Offline</em>
</div><dl class="cl">
<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl><div class="imicn">
<a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="QQ"><img src="static/image/common/qq.gif" alt="QQ" /></a><a href="javascript:;" onclick="window.open('//amos.im.alisoft.com/msg.aw?v=2&uid='+encodeURIComponent('阿里旺旺')+'&site=cntaobao&s=2&charset=utf-8')" title="Wangwang"><img src="static/image/common/taobao.gif" alt="Wangwang" /></a><a href="https://cjhb.site" target="_blank" title="'s Homepage"><img src="static/image/common/forumlink.gif" alt="'s Homepage" /></a><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" title="View details"><img src="static/image/common/userinfo.gif" alt="View details" /></a>
</div>
<div id="avatarfeed"><span id="threadsortswait"></span></div>
</div>
</div>
<div>
<div class="avatar"><a href="home.php?mod=space&uid=2861" class="avtm" target="_blank"><img src="./data/avatar/000/00/28/61_avatar_middle.jpg" class="user_avatar"></a></div>
</div>
<div class="tns xg2"><table cellspacing="0" cellpadding="0"><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=thread&view=me&from=space" class="xi2">3159</a></p>Threads</th><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=reply&view=me&from=space" class="xi2">7941</a></p>Posts</th><td><p><a href="home.php?mod=space&uid=2861&do=profile" class="xi2"><span title="63770">610K</span></a></p>Credits</td></table></div>

<dl class="pil cl">
	<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl>

<dl class="pil cl"><a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="Start QQ chat"><img src="static/image/common/qq_big.gif" alt="QQ" style="margin:0px;"/></a></dl><p style="font-size: 12px;"><a href="thread-10452-1-1.html" rel="nofollow">Show all posts</a></p>
<ul class="xl xl2 o cl">
<li class="pm2"><a href="home.php?mod=spacecp&ac=pm&op=showmsg&handlekey=showmsg_2861&touid=2861&pmid=0&daterange=2&pid=51816&tid=10452" onclick="showWindow('sendpm', this.href);" title="Send PM" class="xi2">Send PM</a></li>
</ul>
</div>
</td>
<td class="plc">
<div class="pi">
<div class="pti">
<div class="pdbt">
</div>
<div class="authi">
<em class="authicn fico-person fic4 fnmr vm" id="authicon51816" title="Author"></em>
 Author<span class="pipe">|</span>
<a href="home.php?mod=space&uid=2861" target="_blank" class="xi2 neiid">hbghlyj</a>

Posted  <em id="authorposton51816">2023-3-18 08:54</em>
</div>
</div>
</div><div class="pct"><div class="pcb">
<div class="t_fsz"><table cellspacing="0" cellpadding="0"><tr><td class="t_f" id="postmessage_51816">
<i class="pstatus">Last edited by hbghlyj 2023-3-18 09:56</i><div class="quote"><blockquote><font size="2"><a href="forum.php?mod=redirect&goto=findpost&pid=51770&ptid=10452" target="_blank"><font color="#999">hbghlyj 发表于 2023-3-17 10:29</font></a></font><br />
图中标的$A',B'$都不是 AB 关于 P 点的反射啊</blockquote></div>4#的图是怎么作的<img src="static/image/smiley/default/shocked.gif" smilieid="6" border="0" alt="" /><br />
</td></tr></table>

</div>
<div id="comment_51816" class="cm">
</div>

</td></tr>
<tr><td class="plc plm">
</td>
</tr>
<tr id="_postposition51816"></tr>
<tr>
<td class="pls"></td>
<td class="plc" style="overflow:visible;">
<div class="po hin">
<div class="pob cl">
<em>
<a class="fastre" href="forum.php?mod=post&action=reply&fid=5&tid=10452&repquote=51816&extra=page%3D1&page=1" onclick="showWindow('reply', this.href)">Reply</a>
<a class="editp" href="forum.php?mod=post&action=edit&fid=5&tid=10452&pid=51816&page=1" onclick="showWindow('edit', this.href, 'get', 0)">Edit</a>
<a class="replyadd"  onclick="showWindow('login','member.php?mod=logging&action=login')" title=""> <span id="review_support_51816"></span></a>
<a class="replysubtract"  onclick="showWindow('login','member.php?mod=logging&action=login')" onmouseover="this.title = ($('review_against_51816').innerHTML ? $('review_against_51816').innerHTML : 0) + ' users'"> <span id="review_against_51816"></span></a>
</em>

</div>
</div>
</td>
</tr>
<tr class="ad">
<td class="pls">
</td>
<td class="plc">
</td>
</tr>
</table>
</div><div id="post_51826" ><table id="pid51826" class="plhin" summary="pid51826" cellspacing="0" cellpadding="0">
<tr>
 <td class="pls" rowspan="2">
<div id="favatar51826" class="pls cl favatar">
<div class="pi">
<div class="authi"><a href="home.php?mod=space&uid=2861" target="_blank" class="xw1">hbghlyj</a>
</div>
</div>
<div class="p_pop blk bui card_gender_2" id="userinfo51826" style="display: none; margin-top: -11px;">
<div class="m z">
<div id="userinfo51826_ma"></div>
</div>
<div class="i y">
<div>
<strong><a href="home.php?mod=space&uid=2861" target="_blank" class="xi2">hbghlyj</a></strong>
<em>Offline</em>
</div><dl class="cl">
<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl><div class="imicn">
<a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="QQ"><img src="static/image/common/qq.gif" alt="QQ" /></a><a href="javascript:;" onclick="window.open('//amos.im.alisoft.com/msg.aw?v=2&uid='+encodeURIComponent('阿里旺旺')+'&site=cntaobao&s=2&charset=utf-8')" title="Wangwang"><img src="static/image/common/taobao.gif" alt="Wangwang" /></a><a href="https://cjhb.site" target="_blank" title="'s Homepage"><img src="static/image/common/forumlink.gif" alt="'s Homepage" /></a><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" title="View details"><img src="static/image/common/userinfo.gif" alt="View details" /></a>
</div>
<div id="avatarfeed"><span id="threadsortswait"></span></div>
</div>
</div>
<div>
<div class="avatar"><a href="home.php?mod=space&uid=2861" class="avtm" target="_blank"><img src="./data/avatar/000/00/28/61_avatar_middle.jpg" class="user_avatar"></a></div>
</div>
<div class="tns xg2"><table cellspacing="0" cellpadding="0"><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=thread&view=me&from=space" class="xi2">3159</a></p>Threads</th><th><p><a href="home.php?mod=space&uid=2861&do=thread&type=reply&view=me&from=space" class="xi2">7941</a></p>Posts</th><td><p><a href="home.php?mod=space&uid=2861&do=profile" class="xi2"><span title="63770">610K</span></a></p>Credits</td></table></div>

<dl class="pil cl">
	<dt>Credits</dt><dd><a href="home.php?mod=space&uid=2861&do=profile" target="_blank" class="xi2">63770</a></dd>
</dl>

<dl class="pil cl"><a href="//wpa.qq.com/msgrd?v=3&uin=15063662&site=Discuz Math Forum&menu=yes&from=discuz" target="_blank" title="Start QQ chat"><img src="static/image/common/qq_big.gif" alt="QQ" style="margin:0px;"/></a></dl><p style="font-size: 12px;"><a href="thread-10452-1-1.html" rel="nofollow">Show all posts</a></p>
<ul class="xl xl2 o cl">
<li class="pm2"><a href="home.php?mod=spacecp&ac=pm&op=showmsg&handlekey=showmsg_2861&touid=2861&pmid=0&daterange=2&pid=51826&tid=10452" onclick="showWindow('sendpm', this.href);" title="Send PM" class="xi2">Send PM</a></li>
</ul>
</div>
</td>
<td class="plc">
<div class="pi">
<div class="pti">
<div class="pdbt">
</div>
<div class="authi">
<em class="authicn fico-person fic4 fnmr vm" id="authicon51826" title="Author"></em>
 Author<span class="pipe">|</span>
<a href="home.php?mod=space&uid=2861" target="_blank" class="xi2 neiid">hbghlyj</a>

Posted  <em id="authorposton51826">2023-3-18 16:21</em>
</div>
</div>
</div><div class="pct"><div class="pcb">
<div class="t_fsz"><table cellspacing="0" cellpadding="0"><tr><td class="t_f" id="postmessage_51826">
<i class="pstatus">Last edited by hbghlyj 2023-4-19 15:32</i><div class="quote"><blockquote><font size="2"><u><font color="#999">TSC999 发表于 2023-3-18 01:50</font></u></font>
4# 楼的图。</blockquote></div>4#的图好像与1#无关吧{:shocked:

Ly-lie · 2023-4-19 21:08

作$A$关于$BC$的对称点$A'$,有$AP'$与$A'P$关于$BC$对称，故$A'P$平行于$DQ$,延长$OD$交$A'P$于$E$,只需$OD=DE$,作$HE'$平行于$DN$交$A'F$于$E'$,$E'G\perp BC$于$G$,$OM\perp BC$于$M$,设$OE'$与$BC$交于$D'$,由$E'H$平行于$AF$得$$ \frac {E'G}{AK}=\frac {FE'}{A'F}=\frac {AH}{AA'}$$得$$ \frac {E'G}{AK}=\frac {2OM}{2AK} $$故$E'G=OM$,即$OD'=E'D'$,故$ ND' $平行于$ E'H $平行于$ AF $平行于$ ND $,得到$ D=D' $,进而$ E=E' $,于是$ OD=DE $,即得证.

kuing · 2023-4-19 22:06

Ly-lie 发表于 2023-4-19 21:08
作$A$关于$BC$的对称点$A'$,有$AP'$与$A'P$关于$BC$对称，故$A'P$平行于$DQ$,延长$OD$交$A'P$于$E$,只需$OD ...

由E'H$平行于$AF$ 这里少了一个 $

另外，本论坛自定义了平行符号命令 \px

Account		Remember me	Forgot password?
Password			Register account

[几何] 反射三角形 九点圆圆心

[几何] 反射三角形九点圆圆心