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1

Part of 2017 Polish MO Finals

Problems(1)

Poland 2017 P1

Source:

4/4/2017
Points PP and QQ lie respectively on sides ABAB and ACAC of a triangle ABCABC and BP=CQBP=CQ. Segments BQBQ and CPCP cross at RR. Circumscribed circles of triangles BPRBPR and CQRCQR cross again at point SS different from RR. Prove that point SS lies on the bisector of angle BACBAC.
geometrycircumcirclegeometry solvedMiquel pointSpiral SimilarityAngle Chasingcyclic quadrilateral