Let ABCD be a convex quadrilateral with AB=CD. From a random point P of it's diagonal BD, we draw a line parallel to AB that intersects AD at point M and a line parallel to CD that intersects BC at point N. Prove that:
a) The sum PM+PN is constant, independent of the position of P on the diagonal BD.
b) MN≤BD. When the equality holds? geometryconstantconvex quadrilateral