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CH and PM meet at the incircle of right triangle ABC

Source: 2021 Sharygin Geometry Olympiad Finals grades X-XI p7

August 2, 2021
concurrentgeometryconcurrenctright trianglegeometry solvedsimilar triangleshumpty points

Problem Statement

Let II be the incenter of a right-angled triangle ABCABC, and MM be the midpoint of hypothenuse ABAB. The tangent to the circumcircle of ABCABC at CC meets the line passing through II and parallel to ABAB at point PP. Let HH be the orthocenter of triangle PABPAB. Prove that lines CHCH and PMPM meet at the incircle of triangle ABCABC.
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