IMO 1970 LL BEL7

Let ABCD be any quadrilateral. A square is constructed on

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IMO 1970 LL BEL7

Origin: BEL

Problem

Let ABCD be any quadrilateral. A square is constructed on each side of the quadrilateral, all in the same manner (i.e., outward or inward). Denote the centers of the squares by M1, M2, M3, and M4. Prove: (a) M1M3 = M2M4; (b) M1M3 is perpendicular to M2M4.