Consider the cube ABCDEFGH and denote by, respectively, M and N the midpoints of [AB] and [CD]. Let P be a point on the line defined by [AE] and Q the point of intersection of the lines defined by [PM] and [BF]. Prove that the triangle [PQN] is isosceles.
https://cdn.artofproblemsolving.com/attachments/0/0/57559efbad87903d087c738df279b055b4aefd.png geometry3D geometryisoscelescube