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Cross-ratio Practice!

Source: 2024 imocsl G3 (Night 6-G)

August 8, 2024
geometryIMOC

Problem Statement

Triangle ABCABC has circumcircle Ω\Omega and incircle ω\omega, where ω\omega is tangent to BC,CA,ABBC, CA, AB at D,E,FD,E,F, respectively. TT is an arbitrary point on ω\omega. EFEF meets BCBC at KK, ATAT meets Ω\Omega again at PP, PKPK meets Ω\Omega again at SS. XX is a point on Ω\Omega such that S,D,XS, D, X are colinear. Let YY be the intersection of AXAX and EFEF, prove that YTYT is tangent to ω\omega.
Proposed by chengbilly
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