ILL 1983 Problem 40

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 $R = a \ ?$