This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 1

2012 International Zhautykov Olympiad, 1
Tags: geometry , geometry question , plane geometry
An acute triangle $ABC$ is given. Let $D$ be an arbitrary inner point of the side $AB$. Let $M$ and $N$ be the feet of the perpendiculars from $D$ to $BC$ and $AC$, respectively. Let $H_1$ and $H_2$ be the orthocentres of triangles $MNC$ and $MND$, respectively. Prove that the area of the quadrilateral $AH_1BH_2$ does not depend on the position of $D$ on $AB$.