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What is the ratio c/a if R = a ?

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October 7, 2010
ratiogeometry3D geometrytetrahedronspherefunctioncongruent triangles

Problem Statement

Four faces of tetrahedron ABCDABCD are congruent triangles whose angles form an arithmetic progression. If the lengths of the sides of the triangles are a<b<ca < b < c, determine the radius of the sphere circumscribed about the tetrahedron as a function on a,ba, b, and cc. What is the ratio c/ac/a if R=a ?R = a \ ?
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