Sharygin Geometry Olympiad 2016 grade 9/2

For discussing Olympiad level Geometry Problems
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Thamim Zahin
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Sharygin Geometry Olympiad 2016 grade 9/2

Unread post by Thamim Zahin » Tue Jan 17, 2017 8:40 pm

Let $H$ be the orthocenter of an acute-angled triangle $ABC$. Point $X_A$ lying on the tangent at $H$ to the circumcircle of triangle $BHC$ is such that $AH=AX_A$ and $X_A \not= H$. Points $X_B,X_C$ are defined similarly. Prove that the triangle $X_AX_BX_C$ and the orthotriangle of $ABC$ are similar.
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