MathDB

G7

Part of 2024-IMOC

Problems(1)

Hong Kong Jane Street

Source: 2024 imocsl G7 (Boring Competiton P1)

8/8/2024
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
geometryIMOC