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AB, SH , TR concurrent wanted , HAPQ and SACQ are #

Source: 2023 IGO Intermediate P4

January 18, 2024
geometryconcurrencyconcurrent

Problem Statement

Let ABCABC be a triangle and PP be the midpoint of arc BACBAC of circumcircle of triangle ABCABC with orthocenter HH. Let Q,SQ, S be points such that HAPQHAPQ and SACQSACQ are parallelograms. Let TT be the midpoint of AQAQ, and RR be the intersection point of the lines SQSQ and PBPB. Prove that ABAB, SHSH and TRTR are concurrent.
Proposed by Dominik Burek - Poland
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