IMO 2022 Shortlist G4
Let ABC be an acute-angled triangle with AC ą AB, let O be its circumcentre, and let D be a point on the segment BC. The...
Category: Geometry
Problem
Let ABC be an acute-angled triangle with AC ą AB, let O be its circumcentre, and let D be a point on the segment BC. The line through D perpendicular to BC intersects the lines AO, AC and AB at W, X and Y , respectively. The circumcircles of triangles AXY and ABC intersect again at Z ‰ A. Prove that if OW “ OD, then DZ is tangent to the circle AXY . (United Kingdom)