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(BAC)^2+(CAD)^2 +(DAB)^2=(BCD)^2 for tetrahedron, <BAC=<CAD=<DAB=90^o

Source: Norwegian Mathematical Olympiad 2021 - Abel Competition p4a

May 29, 2021
geometry3D geometrytetrahedronright angles

Problem Statement

A tetrahedron ABCDABCD satisfies ∠BAC=∠CAD=∠DAB=90o\angle BAC=\angle CAD=\angle DAB=90^o. Show that the areas of its faces satisfy the equation area(BAC)2+area(CAD)2+area(DAB)2=area(BCD)2area(BAC)^2 + area(CAD)^2 + area(DAB)^2 = area(BCD)^2. .
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