A. 581. In the plane, there are given two circles k1 and k2 with different radii, and a point O lying outside the circles. The end-points of the tangents drawn from O to k1 are P and Q, the end-points of the tangents drawn from O to k2 are R and S. The points P, Q, R, S are distinct. Let H be the external homothety center between k1 and k2. Prove that if PR is not a external common tangent to the circles but passes through H then QS also passes through H.
Deadline expired on 11 March 2013.