Problem

Source: Mexico 2023/3

Tags: geometry, 2023, P3, Mexico, Hi



Let ABCD be a convex quadrilateral. If M,N,K are the midpoints of the segments AB,BC, and CD, respectively, and there is also a point P inside the quadrilateral ABCD such that, BPN=PAD and CPN=PDA. Show that ABCD=4PMPK.