The circles (R,r) and (P,ρ), where r>ρ, touch externally at A. Their direct common tangent touches (R,r) at B and (P,ρ) at C. The line RP meets the circle (P,ρ) 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∣. arithmetic sequencegeometry