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pair of equal angles given, right angle wanted, circumcenter related

Source: Polish second round 1999 p4

January 19, 2020
geometryequal anglesright angleCircumcenter

Problem Statement

Let PP be a point inside a triangle ABCABC such that ∠PAB=∠PCA\angle PAB = \angle PCA and ∠PAC=∠PBA\angle PAC = \angle PBA. If O≠PO \ne P is the circumcenter of △ABC\triangle ABC, prove that ∠APO\angle APO is right.
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