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Source: 2024 imocsl G7 (Boring Competiton P1)

August 8, 2024
geometryIMOC

Problem Statement

Triangle ABCABC has circumcenter OO and incenter II. The incircle is tangent to AC,ABAC, AB at E,FE, F, respectively. HH is the orthocenter of △BIC\triangle BIC. ⊙(AEF)\odot(AEF) and ⊙(ABC)\odot(ABC) intersects again at SS. BC,AHBC, AH intersects OIOI again at J,KJ, K, respectively. Prove that H,K,J,SH, K, J, S are concyclic.
Proposed by chengbilly
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