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anglechasing , circumcenter wanted

Source: Sharygin 2011 Final 9.2

December 16, 2018
geometrycircumcircleAngle Chasingperpendicular bisector

Problem Statement

In triangle ABC,∠B=2∠CABC, \angle B = 2\angle C. Points PP and QQ on the medial perpendicular to CBCB are such that ∠CAP=∠PAQ=∠QAB=∠A3\angle CAP = \angle PAQ = \angle QAB = \frac{\angle A}{3} . Prove that QQ is the circumcenter of triangle CPBCPB.
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