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Found problems: 1

2021 Sharygin Geometry Olympiad, 10-11.7
Tags: concurrent , geometry , concurrenct , right triangle , geometry solved , similar triangles , humpty points
Let $I$ be the incenter of a right-angled triangle $ABC$, and $M$ be the midpoint of hypothenuse $AB$. The tangent to the circumcircle of $ABC$ at $C$ meets the line passing through $I$ and parallel to $AB$ at point $P$. Let $H$ be the orthocenter of triangle $PAB$. Prove that lines $CH$ and $PM$ meet at the incircle of triangle $ABC$.