MathDB

8.6

Part of 2021 Sharygin Geometry Olympiad

Problems(1)

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

Source: 2021 Sharygin Geometry Olympiad Finals grade VIII p6

8/2/2021
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).
geometryCircumcenterequal segmentsConcyclic