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equifacial tetrahedron and circumcircles of faces

Source: RMO District 2005, 8th Grade, Problem 3

March 5, 2005
geometry3D geometrytetrahedroncircumcircletrigonometrytrig identitiesLaw of Sines

Problem Statement

Prove that if the circumcircles of the faces of a tetrahedron ABCDABCD have equal radii, then AB=CDAB=CD, AC=BDAC=BD and AD=BCAD=BC.
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