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a parallelogram and a common point of some circles

Source: ARO 2005 - 9.1

April 30, 2005
geometryparallelogramcircumcirclegeometric transformationreflectionperpendicular bisectorangle bisector

Problem Statement

Given a parallelogram ABCDABCD with AB<BCAB<BC, show that the circumcircles of the triangles APQAPQ share a second common point (apart from AA) as P,QP,Q move on the sides BC,CDBC,CD respectively s.t. CP=CQCP=CQ.
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