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Q symmetric of P wrt BH wanted, orthocenter related

Source: 2023 Czech-Polish-Slovak Match Junior, individual p3 CPSJ

May 5, 2024
geometryorthocenter

Problem Statement

Given is an acute triangle ABCABC. Point PP lies inside this triangle and lies on the bisector of angle ∠BAC\angle BAC. Suppose that the point of intersection of the altitudes HH of triangle ABPABP lies inside triangle ABCABC. Let QQ be the intersection of the line APAP and the line perpendicular to ACAC passing through HH. Prove that QQ is the point symmetrical to PP wrt the line BHBH.
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