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SSSS and diagonals perpendicular

Source: Serbia & Montenegro 2001 1st Grade P1

June 1, 2021
geometry

Problem Statement

Let ABCDABCD and A1B1C1D1A_1B_1C_1D_1 be convex quadrangles in a plane, such that AB=A1B1AB=A_1B_1, BC=B1C1BC=B_1C_1, CD=C1D1CD=C_1D_1 and DA=D1A1DA=D_1A_1. Given that diagonals ACAC and BDBD are perpendicular to each other, prove that the same holds for diagonals A1C1A_1C_1 and B1D1B_1D_1.
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