Circles C1 and C2 with centers O1 and O2, respectively, are externally tangent at point λ. A circle C with center O touches C1 at A and C2 at B so that the centers O1, O2 lie inside C. The common tangent to C1 and C2 at λ intersects the circle C at K and L. If D is the midpoint of the segment KL, show that ∠O1OO2=∠ADB.
Greece geometryincentercircumcirclegeometry proposed