IMO 1985 LL CYP18

Origin: CYP

Problem

The circles (R, r) and (P, \rho), where r > \rho, touch externally at A. Their direct common tangent touches (R, r) at B and (P, \rho) at C. The line RP meets the circle (P, \rho) again at D and the line BC at E. If |BC| = 6|DE|, prove that: (a) the lengths of the sides of the triangle RBE are in an arithmetic progression, and (b) |AB| = 2|AC|.