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Squares Constructed on Sides of Quadrilateral

Source: ILL 1970 - Problem 7.

May 24, 2011
geometrygeometry proposed

Problem Statement

Let ABCDABCD be an arbitrary quadrilateral. Squares with centers M1,M2,M3,M4M_1, M_2, M_3, M_4 are constructed on AB,BC,CD,DAAB,BC,CD,DA respectively, all outwards or all inwards. Prove that M1M3=M2M4M_1 M_3=M_2 M_4 and M1M3⊥M2M4M_1 M_3\perp M_2 M_4.
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