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IMO ShortList 2002, geometry problem 1

Source: IMO ShortList 2002, geometry problem 1

September 28, 2004
geometrycircumcirclehomothetyincenterIMO Shortlistgeometry solvedtangent circles

Problem Statement

Let BB be a point on a circle S1S_1, and let AA be a point distinct from BB on the tangent at BB to S1S_1. Let CC be a point not on S1S_1 such that the line segment ACAC meets S1S_1 at two distinct points. Let S2S_2 be the circle touching ACAC at CC and touching S1S_1 at a point DD on the opposite side of ACAC from BB. Prove that the circumcentre of triangle BCDBCD lies on the circumcircle of triangle ABCABC.
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