IMO Shortlist 1998 problem G8
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Avg: 9,0 Let be a triangle such that and . The tangent at to the circumcircle of triangle meets the line at . Let be the reflection of in the line , let be the foot of the perpendicular from to , and let be the midpoint of the segment . Let the line intersect the circle again at .
Prove that the line is tangent to the circumcircle of triangle .
commentEdited by Orl.
Prove that the line is tangent to the circumcircle of triangle .
commentEdited by Orl.
Izvor: Međunarodna matematička olimpijada, shortlist 1998