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Reflection of a Point lying on Circumcircle

Source: Tournament of Towns Spring 2015 Senior A-level

February 24, 2017
geometrygeometric transformationreflectioncircumcircle

Problem Statement

A point XX is marked on the base BCBC of an isosceles △ABC\triangle ABC, and points PP and QQ are marked on the sides ABAB and ACAC so that APXQAPXQ is a parallelogram. Prove that the point YY symmetrical to XX with respect to line PQPQ lies on the circumcircle of the △ABC\triangle ABC. (55 points)
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