IMO 2024 Shortlist G7
Let ABC be a triangle with incentre I such that AB ă AC ă BC. The second intersections of AI, BI, and CI with the circum...
Category: Geometry
Problem
Let ABC be a triangle with incentre I such that AB ă AC ă BC. The second intersections of AI, BI, and CI with the circumcircle of triangle ABC are MA, MB, and MC, respectively. Lines AI and BC intersect at D and lines BMC and CMB intersect at X. Suppose the circumcircles of triangles XMBMC and XBC intersect again at S ‰ X. Lines BX and CX intersect the circumcircle of triangle SXMA again at P ‰ X and Q ‰ X, respectively. Prove that the circumcentre of triangle SID lies on PQ. (Thailand)