Let Γ and Γ1 be two circles internally tangent at A, with centers O and O1 and radii r and r1, respectively (r>r1). B is a point diametrically opposed to A in Γ, and C is a point on Γ such that BC is tangent to Γ1 at P. Let A′ the midpoint of BC. Given that O1A′ is parallel to AP, find the ratio r/r1. ratiogeometry proposedgeometry