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L,T,F are collinear iff B,E,A,R are concyclic.

Source: 2022 IMOC G2 https://artofproblemsolving.com/community/c6h2918249p26069468

September 5, 2022
geometrycollinearConcyclic

Problem Statement

The incenter of triangle ABCABC is I I. the circumcircle of ABCABC is tangent to BCBC, CACA, ABAB at T,E,FT, E, F. RR is a point on BCBC . Let the CC-excenter of △CER\vartriangle CER be LL. Prove that points L,T,FL,T,F are collinear if and only if B,E,A,RB,E,A,R are concyclic.
proposed by kyou46
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