IMO 2007 Shortlist G5
Let ABC be a fixed triangle, and let A1, B1, C1 be the midpoints of sides BC, CA, AB, respectively. Let P be a variable ...
Category: Geometry
Problem
Let ABC be a fixed triangle, and let A1, B1, C1 be the midpoints of sides BC, CA, AB, respectively. Let P be a variable point on the circumcircle. Let lines PA1, PB1, PC1 meet the circumcircle again at A0 , B0 , C0 respectively. Assume that the points A, B, C, A0 , B0 , C0 are distinct, and lines AA0 , BB0 , CC0 form a triangle. Prove that the area of this triangle does not depend on P. (United Kingdom)