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AB^2+BC^2+CD^2+DA^2 = AC^2+BD^2+4MN^2 in 3D, with midpoints

Source: Austrian-Polish 1979

May 25, 2019
geometry3D geometrymidpoints

Problem Statement

Let A,B,C,DA,B,C,D be four points in space, and MM and NN be the midpoints of ACAC and BDBD, respectively. Show that AB2+BC2+CD2+DA2=AC2+BD2+4MN2AB^2+BC^2+CD^2+DA^2 = AC^2+BD^2+4MN^2
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