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2013 preRMO p15, midpoints of segments of midpoints of ABCD, rectangle

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August 8, 2019
geometryrectangle

Problem Statement

Let A1,B1,C1,D1A_1,B_1,C_1,D_1 be the midpoints of the sides of a convex quadrilateral ABCDABCD and let A2,B2,C2,D2A_2, B_2, C_2, D_2 be the midpoints of the sides of the quadrilateral A1B1C1D1A_1B_1C_1D_1. If A2B2C2D2A_2B_2C_2D_2 is a rectangle with sides 44 and 66, then what is the product of the lengths of the diagonals of ABCDABCD ?
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