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if MNPQ is square, then ABCD is also square

Source: Romania TST 1995 2.3

February 17, 2020
geometrysquare

Problem Statement

Let M,N,P,QM, N, P, Q be points on sides AB,BC,CD,DAAB, BC, CD, DA of a convex quadrilateral ABCDABCD such that AQ=DP=CN=BMAQ = DP = CN = BM. Prove that if MNPQMNPQ is a square, then ABCDABCD is also a square.
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