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Sharygin CR 2019 P7

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March 6, 2019
geometry

Problem Statement

Let AHAAH_A, BHBBH_B, CHCCH_C be the altitudes of the acute-angled ΔABC\Delta ABC. Let XX be an arbitrary point of segment CHCCH_C, and PP be the common point of circles with diameters HCXH_CX and BC, distinct from HCH_C. The lines CPCP and AHAAH_A meet at point QQ, and the lines XPXP and ABAB meet at point RR. Prove that A,P,Q,R,HBA, P, Q, R, H_B are concyclic.
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