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O lies on the circumcircle of ABC

Source: Italy TST 2003

November 9, 2010
geometrycircumcirclegeometry unsolved

Problem Statement

Let B≠AB\not= A be a point on the tangent to circle S1S_1 through the point AA on the circle. A point CC outside the circle is chosen so that segment ACAC intersects the circle in two distinct points. Let S2S_2 be the circle tangent to ACAC at CC and to S1S_1 at some point DD, where DD and BB are on the opposite sides of the line ACAC. Let OO be the circumcentre of triangle BCDBCD. Show that OO lies on the circumcircle of triangle ABCABC.
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