R lies on AC wanted, starting with cyclic ABCD, 2 circumcenters,
Source: 2020 XXV All-Ukrainian Correspondence MO grades 5-12 p11
April 29, 2021
geometrycollinearcyclic quadrilateralUkraine Correspondence
Problem Statement
The diagonals of the cyclic quadrilateral intersect at the point . Let and are the centers of the circles circumscribed around the triangles and , respectively. A straight line passing through the point parallel to , and a straight line passing through the point parallel to , intersect at the point . Prove that the point lies on segment .