IMO 2013 Shortlist G1
Let ABC be an acute-angled triangle with orthocenter H, and let W be a point on side BC. Denote by M and N the feet of t...
Category: Geometry
Problem
Let ABC be an acute-angled triangle with orthocenter H, and let W be a point on side BC. Denote by M and N the feet of the altitudes from B and C, respectively. Denote by ω1 the circumcircle of BWN, and let X be the point on ω1 which is diametrically opposite to W. Analogously, denote by ω2 the circumcircle of CWM, and let Y be the point on ω2 which is diametrically opposite to W. Prove that X, Y and H are collinear. (Thaliand)