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Tetrahedron with all faces equal and unit curcumsphere

Source: Problem 3, Brazilian MO, 1990

March 19, 2006
geometry3D geometrytetrahedroncircumcirclespherePythagorean Theoremgeometry proposed

Problem Statement

Each face of a tetrahedron is a triangle with sides a,b,a, b,c and the tetrahedon has circumradius 1. Find a2+b2+c2a^2 + b^2 + c^2.
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