Let A,B be two distinct points on a given circle O and let P be the midpoint of the line segment AB. Let O1 be the circle tangent to the line AB at P and tangent to the circle O. Let l be the tangent line, different from the line AB, to O1 passing through A. Let C be the intersection point, different from A, of l and O. Let Q be the midpoint of the line segment BC and O2 be the circle tangent to the line BC at Q and tangent to the line segment AC. Prove that the circle O2 is tangent to the circle O. trigonometrygeometrycircumcirclegeometry unsolved