IMO 2022 Shortlist G8
Let AA1 BCC1 B1 be a convex cyclic hexagon such that AC is tangent to the incircle of the triangle A1 B1 C1 , and A1 C1 ...
Category: Geometry
Problem
Let AA1 BCC1 B1 be a convex cyclic hexagon such that AC is tangent to the incircle of the triangle A1 B1 C1 , and A1 C1 is tangent to the incircle of the triangle ABC. Let the lines AB and A1 B1 meet at X and let the lines BC and B1 C1 meet at Y . Prove that if XBY B1 is a convex quadrilateral, then it has an incircle. (Australia) Shortlisted problems 7