IMO 1984 LL USA62
From a point P exterior to a circle K, two rays are drawn
IMO 1984 LL USA62
Origin: USA
Problem
From a point P exterior to a circle K, two rays are drawn intersecting K in the respective pairs of points A, A′ and B, B′. For any other pair of points C, C′ on K, let D be the point of intersection of the circumcircles of triangles PAC and PB′C′ other than point P. Similarly, let D′ be the point of intersection of the circumcircles of triangles PA′C′ and PBC other than point P. Prove that the points P, D, and D′ are collinear.