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Variants of Stainer

Source: 45th International Tournament of Towns, Senior O-Level P4, Fall 2023

December 16, 2023
geometry

Problem Statement

4. Given is an acute-angled triangle ABC,HA B C, H is its orthocenter. Let PP be an arbitrary point inside (and not on the sides) of the triangle ABCA B C that belongs to the circumcircle of the triangle ABHA B H. Let A′,B′A^{\prime}, B^{\prime}, C′C^{\prime} be projections of point PP to the lines BC,CA,ABB C, C A, A B. Prove that the circumcircle of the triangle A′B′C′A^{\prime} B^{\prime} C^{\prime} passes through the midpoint of segment CPC P. Alexey Zaslavsky
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