Sharygin 2006, correspondence round, problem 18
Sharygin 2006, correspondence round, problem 18 is a plane geometry problem from the Sharygin Geometry Olympiad 2006, correspondence round, problem 18 (grades 9–11): two perpendicular lines through the orthocenter.
Problem
Two perpendicular lines are drawn through the orthocenter $H$ of the triangle $ABC$. One of them intersects $BC$ at point $X$, another one intersects $AC$ in point $Y$. The lines $AZ$, $BZ$ are parallel to the lines $HX$ and $HY$ respectively. Prove that the points $X$, $Y$, $Z$ are collinear.
Source Sharygin Geometry Olympiad 2006, correspondence round, problem 18 (grades 9–11)
The diagram
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