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Intersection of two circles in an isosceles triangle

Source: 2019 Baltic Way P11

November 18, 2019
geometry

Problem Statement

Let ABCABC be a triangle with AB=ACAB = AC. Let MM be the midpoint of BCBC. Let the circles with diameters ACAC and BMBM intersect at points MM and PP. Let MPMP intersect ABAB at QQ. Let RR be a point on APAP such that QR∥BPQR \parallel BP. Prove that CPCP bisects ∠RCB\angle RCB.
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