Page 1 of 1

APMO 2016 #1

Posted: Fri Aug 05, 2016 10:11 am
by Zawadx
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 $AB = AC$.

Re: APMO 2016 #1

Posted: Fri Aug 05, 2016 10:12 am
by Zawadx
Hint:
It's a geometric functional equation! :D