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Circumcircles and Reflections

Source: 2013 CMO #5

March 31, 2013
geometrycircumcirclegeometric transformationreflectionsymmetrytrigonometryrhombus

Problem Statement

Let OO denote the circumcentre of an acute-angled triangle ABCABC. Let point PP on side ABAB be such that ∠BOP=∠ABC\angle BOP = \angle ABC, and let point QQ on side ACAC be such that ∠COQ=∠ACB\angle COQ = \angle ACB. Prove that the reflection of BCBC in the line PQPQ is tangent to the circumcircle of triangle APQAPQ.
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