IMO Shortlist 2002 problem G1

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Dodao/la: arhiva
April 2, 2012
Let B be a point on a circle S_1, and let A be a point distinct from B on the tangent at B to S_1. Let C be a point not on S_1 such that the line segment AC meets S_1 at two distinct points. Let S_2 be the circle touching AC at C and touching S_1 at a point D on the opposite side of AC from B. Prove that the circumcentre of triangle BCD lies on the circumcircle of triangle ABC.
Source: Međunarodna matematička olimpijada, shortlist 2002