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[几何] 抛物线倒演简易结论角相等

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1+1=? posted 2025-6-16 14:54 from mobile |Read mode
已知抛物线$y^2=2px$上有两点$A,B$,弦$AB$及$A$点切线分别与直线$x=-2p$交于$C,D$二点,抛物线顶点为$O$点,则$\angle AOB$与$\angle COD$相等或互补. 1000093419.jpg

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original poster 1+1=? posted 2025-6-16 17:16 from mobile
结论二
已知抛物线$y^2=2px$的顶点为$O$点,作点$A$的切线及其极线分别与直线$x=-2p$交于$D$,$E$,$F$三点,切点为$B,C$二点,则直线$FO$平分$\angle EOD$的外角(补角). 1000093421.jpg

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original poster 1+1=? posted 2025-6-16 19:45 from mobile
结论三
已知抛物线$y^2=2px$的顶点为$O$点,点$A$关于抛物线的两条切线与点$P=(2p,0)$的极线交于$B$,$C$二点,直线$PA$与$P$点极线交于$D$点,则$DO$平分$\angle BOC$或其外角.

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