Forgot password
 Register account
View 2064|Reply 2

[几何] 内心和垂足的连线平行于旁切圆切点和弧中点的连线

[Copy link]

3200

Threads

7827

Posts

52

Reputation

Show all posts

hbghlyj posted 2020-7-29 19:05 |Read mode
Screenshot_2020_0729_185900.png
I、I'分别是△ABC的内心和旁心,D是II'中点,AH是高,E是旁切圆在BC上的切点,求证:DE∥HI

3200

Threads

7827

Posts

52

Reputation

Show all posts

original poster hbghlyj posted 2020-7-29 19:05
手机geogebra和手机上论坛真是方便啊!

3200

Threads

7827

Posts

52

Reputation

Show all posts

original poster hbghlyj posted 2020-7-31 23:08
$\dfrac{AH}{I'E}=\dfrac{AH}{\dfrac{a·AH}{b+c-a}}=\dfrac{b+c-a}a$
$\dfrac{AI}{I'D}=\dfrac{2\dfrac{AI}{AI'}}{1-\dfrac{AI}{AI'}}=\dfrac{2\dfrac{b+c-a}{a+b+c}}{1-\dfrac{b+c-a}{a+b+c}}=\dfrac{b+c-a}a$
$\therefore\frac{AH}{I'E}=\frac{AI}{I'D}$.
又AH∥I'E,∴△AIH~△I'DE,∴DE∥HI

Quick Reply

Advanced Mode
B Color Image Link Quote Code Smilies
You have to log in before you can reply Login | Register account

$\LaTeX$ formula tutorial

Mobile version

2025-7-15 13:59 GMT+8

Powered by Discuz!

Processed in 0.014967 seconds, 25 queries