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Geometry problem number 4 IMO 2013 Colombia

Submitted by Structure on Wed, 07/31/2013 - 08:49.

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. $ \omega_1 $ is the circumcircle of triangle BWN, and X is a point such that WX is a diameter of $ \omega_1 $. Similarly, $ \omega_2 $ is the circumcircle of triangle CWM, and Y is a point such that WY is a diameter of $ \omega_2 $. Show that the points X, Y, and H are collinear.

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