IMO 2023 Shortlist G2
Let ABC be a triangle with AC ą BC. Let ω be the circumcircle of triangle ABC and let r be the radius of ω. Point P lies...
Category: Geometry
Problem
Let ABC be a triangle with AC ą BC. Let ω be the circumcircle of triangle ABC and let r be the radius of ω. Point P lies on segment AC such that BC “ CP and point S is the foot of the perpendicular from P to line AB. Let ray BP intersect ω again at D and let Q lie on line SP such that PQ “ r and S,P,Q lie on the line in that order. Finally, let the line perpendicular to CQ from A intersect the line perpendicular to DQ from B at E. Prove that E lies on ω. (Iran)