IMO 2019 Shortlist G3
In triangle ABC, let A1 and B1 be two points on sides BC and AC, and let P and Q be two points on segments AA1 and BB1, ...
Category: Geometry
Problem
In triangle ABC, let A1 and B1 be two points on sides BC and AC, and let P and Q be two points on segments AA1 and BB1, respectively, so that line PQ is parallel to AB. On ray PB1, beyond B1, let P1 be a point so that =PP1C “ =BAC. Similarly, on ray QA1, beyond A1, let Q1 be a point so that =CQ1Q “ =CBA. Show that points P, Q, P1, and Q1 are concyclic. (Ukraine)