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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 \omega_1 the circumcircle of BWN, and let X be the point on \omega_1 which is diametrically opposite to W. Analogously, denote by \omega_2 the circumcircle of CWM, and let Y be the point on \omega_2 which is diametrically opposite to W. Prove that X, Y and H are collinear.

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