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equal segments concerning circumcircle

Source: IGO Elementary 2016 2

July 22, 2018
geometryequal segmentscircumcircleAngle Chasing

Problem Statement

Let ω\omega be the circumcircle of triangle ABCABC with AC>ABAC > AB. Let XX be a point on ACAC and YY be a point on the circle ω\omega, such that CX=CY=ABCX = CY = AB. (The points AA and YY lie on different sides of the line BCBC). The line XYXY intersects ω\omega for the second time in point PP. Show that PB=PCPB = PC.
by Iman Maghsoudi
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