MathDB

2

Part of 2018 Japan MO Finals

Problems(1)

Equal lengths and concurrency on circle

Source: Japan Mathematical Olympiad Finals 2018 Q2

2/13/2018
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.
geometrycircumcirclereflectionpower of a pointSpiral Similarity