Through the vertex A of a triangle ABC a straight line AM is
drawn, cutting the side BC in M. Let O and I be the centers of
the circumscribed circle O and the inscribed circle I of
ABC. The circle w1 and w2 with centers w1 and w2 are
each tangent to O and the first is tangent also to two sides of
<AMB, while the second is tangent to the two sides of <AMC. Prove that the straight line joining w1 and w2 passes
through I.