IMO 2011 Shortlist G4
Let ABC be an acute triangle with circumcircle Ω. Let B0 be the midpoint of AC and let C0 be the midpoint of AB. Let D b...
Category: Geometry
Problem
Let ABC be an acute triangle with circumcircle Ω. Let B0 be the midpoint of AC and let C0 be the midpoint of AB. Let D be the foot of the altitude from A, and let G be the centroid of the triangle ABC. Let ω be a circle through B0 and C0 that is tangent to the circle Ω at a point X 6= A. Prove that the points D, G, and X are collinear.