APMO 2016 #1

Discussion on Asian Pacific Mathematical Olympiad (APMO)
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Zawadx
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APMO 2016 #1

Unread post by Zawadx » Fri Aug 05, 2016 10:11 am

We say that a triangle $ABC$ is great if the following holds: for any point $D$ on the side $BC$, if $P$ and $Q$ are the feet of the perpendiculars from $D$ to the lines $AB$ and $AC$, respectively, then the reflection of $D$ in the line $PQ$ lies on the circumcircle of the triangle $ABC$. Prove that triangle $ABC$ is great if and only if $\angle A = 90^{\circ}$ and $AB = AC$.

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Zawadx
Posts: 90
Joined: Fri Dec 28, 2012 8:35 pm

Re: APMO 2016 #1

Unread post by Zawadx » Fri Aug 05, 2016 10:12 am

Hint:
It's a geometric functional equation! :D

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