IMO 1983 LL LUX40

Four faces of tetrahedron ABCD are congruent triangles whose

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IMO 1983 LL LUX40

Origin: LUX

Problem

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