IMO 1971 LL BUL9

Origin: BUL

Problem

The base of an inclined prism is a triangle ABC. The per- pendicular projection of B1, one of the top vertices, is the midpoint of BC. The dihedral angle between the lateral faces through BC and AB is \alpha, and the lateral edges of the prism make an angle \beta with the base. If r1, r2, r3 are exradii of a perpendicular section of the prism, assuming that in ABC, cos2 A + cos2 B + cos2 C = 1, \angleA < \angleB < \angleC, and BC = a, calculate r1r2 + r1r3 + r2r3.