# IMO 2013 Problem 4

Let ABC be an acute triangle with orthocenter H, and let{ W be a point on the side BC, lying strictly between B and C. The points M and N are the feet of the altitudes from B and C, respectively. Denote by \omega_1 is the circumcircle of BWN, and let X be the point on \omega_1 such that WX is a diameter of \omega_1. Analogously, denote by \omega_2 the circumcircle of triangle CWM, and let Y be the point such that WY is a diameter of \omega_2.

Prove that X, Y and H are collinear.

I placed a solution on a separate page separate page. There is also a second, synthetic solution.