## Geometry problem number 4 IMO 2013 Colombia

Posted July 31st, 2013 by Structure

Let ABC be an acute triangle with orthocenter H, and let W be a point on the side BC, between B and C. The points M and N are the feet of the altitudes drawn from B and C, respectively. is the circumcircle of triangle BWN, and X is a point such that WX is a diameter of . Similarly, is the circumcircle of triangle CWM, and Y is a point such that WY is a diameter of . Show that the points X, Y, and H are collinear.