IMO Shortlist 2002 problem G1
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Avg: 6,0 Let be a point on a circle , and let be a point distinct from on the tangent at to . Let be a point not on such that the line segment meets at two distinct points. Let be the circle touching at and touching at a point on the opposite side of from . Prove that the circumcentre of triangle lies on the circumcircle of triangle .
Izvor: Međunarodna matematička olimpijada, shortlist 2002