In the triangle ABC, we have that M and N are points on AB and AC, respectively, such that BC is parallel to MN. A point D is chosen inside the triangle AMN. Let E and F be the points of intersection of MN with BD and CD, respectively. Show that the line joining the centers of the circles circumscribed to the triangles DEN and DFM is perpendicular to AD.
Problem
Source: Mathematics Regional Olympiad of Mexico Center Zone 2015 P5
Tags: geometry, perpendicular