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circumcenter of ABC lies on circle (PXQ), AP = AB, PB // AC, AQ = AC, CQ // AB

Source: 2021 Sharygin Geometry Olympiad Finals grade VIII p6

August 2, 2021
geometryCircumcenterequal segmentsConcyclic

Problem Statement

Let ABCABC be an acute-angled triangle. Point PP is such that AP=ABAP = AB and PB∥ACPB\parallel AC. Point QQ is such that AQ=ACAQ = AC and CQ∥ABCQ\parallel AB. Segments CPCP and BQBQ meet at point XX. Prove that the circumcenter of triangle ABCABC lies on the circle (PXQ)(PXQ).
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