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PY bisects AX, feet of altitudes, intersections of circumcircles AXC and PQC

Source: 2020 NZMO Round 1 p6

January 10, 2021
geometrybisects segment

Problem Statement

Let △ABC\vartriangle ABC be an acute triangle with AB>ACAB > AC. Let PP be the foot of the altitude from CC to ABAB and let QQ be the foot of the altitude from BB to ACAC. Let XX be the intersection of PQPQ and BCBC. Let the intersection of the circumcircles of triangle △AXC\vartriangle AXC and triangle △PQC\vartriangle PQC be distinct points: CC and YY . Prove that PYPY bisects AXAX.
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