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reflection of BC wrt PQ is tangent to (APQ), <POB = <ABC , <QOC = <ACB

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 3.6

September 23, 2021
geometryreflectiontangentequal angles

Problem Statement

Let △ABC\vartriangle ABC be a triangle with circumcenter OO. Let P P and QQ be internal points on the sides ABAB and ACAC respectively such that ∠POB=∠ABC\angle POB = \angle ABC and ∠QOC=∠ACB\angle QOC = \angle ACB. Show that the reflection of line BCBC over line PQPQ is tangent to the circumcircle of triangle △APQ\vartriangle APQ.
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