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

Source: 2022 Saudi Arabia January Camp Test 2.1 BMO + EGMO TST

November 1, 2022
geometryCircumcenter

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 circumcircle of triangle PXQPXQ.
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