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(STX) bisects BC

Source: 2022 IMOC G5 https://artofproblemsolving.com/community/c6h2918249p26069468

September 5, 2022
geometrymidpointConcyclic

Problem Statement

PP is a point inside ABCABC. BPBP, CPCP intersect AC,ABAC, AB at E,FE, F, respectively. APAP intersect ⊙(ABC)\odot (ABC) again at X. ⊙(ABC)\odot (ABC) and ⊙(AEF)\odot (AEF) intersect again at SS. TT is a point on BCBC such that PT∥EFP T \parallel EF. Prove that ⊙(STX)\odot (ST X) passes through the midpoint of BCBC.
proposed by chengbilly
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