IMO 2024 Shortlist G8
Let ABC be a triangle with AB ă AC ă BC, and let D be a point in the interior of segment BC. Let E be a point on the cir...
Category: Geometry
Problem
Let ABC be a triangle with AB ă AC ă BC, and let D be a point in the interior of segment BC. Let E be a point on the circumcircle of triangle ABC such that A and E lie on opposite sides of line BC and =BAD “ =EAC. Let I, IB, IC, JB, and JC be the incentres of triangles ABC, ABD, ADC, ABE, and AEC, respectively. Prove that IB, IC, JB, and JC are concyclic if and only if AI, IBJC, and JBIC concur. (Canada) Shortlisted problems 9