IMO 1989 LL BUL6

Origin: BUL

Problem

The circles c1 and c2 are tangent at the point A. A straight line l through A intersects c1 and c2 at points C1 and C2 respectively. A circle c, which contains C1 and C2, meets c1 and c2 at points B1 and B2 respectively. Let \kappa be the circle circumscribed around triangle AB1B2. The circle k tangent to \kappa at the point A meets c1 and c2 at the points D1 and D2 respectively. Prove that (a) the points C1, C2, D1, D2 are concyclic or collinear; (b) the points B1, B2, D1, D2 are concyclic if and only if AC1 and AC2 are diameters of c1 and c2.