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two squares, one given, one wanted

Source: Argentina 1994 OMA L3 p3

May 13, 2024
geometrySquares

Problem Statement

Given in the plane the square ABCDABCD, the square A1B1C1D1A_1B_1C_1D_1, smaller than the first, and a quadrilateral PQRSPQRS that satisfy the following conditions ∙\bullet ABCDABCD and A1B1C1D1A_1B_1C_1D_1 have a common center and respectively parallel sides. ∙\bulletPP, QQ, RR, SS belong one to each side of the square ABCDABCD. ∙\bullet A1A_1, B1B_1, C1C_1, D1D_1 belong one to each side of the quadrilateral PQRSPQRS. Prove that PQRSPQRS is a square.
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