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Equal lengths and concurrency on circle

Source: Japan Mathematical Olympiad Finals 2018 Q2

February 13, 2018
geometrycircumcirclereflectionpower of a pointSpiral Similarity

Problem Statement

Given a scalene triangle △ABC\triangle ABC, D,ED,E lie on segments AB,ACAB,AC respectively such that CA=CD,BA=BECA=CD, BA=BE. Let ω\omega be the circumcircle of △ADE\triangle ADE. PP is the reflection of AA across BCBC, and PD,PEPD,PE meets ω\omega again at X,YX,Y respectively. Prove that BXBX and CYCY intersect on ω\omega.
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