IMO Shortlist 2006 problem G2


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2. travnja 2012.
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Let ABC be a trapezoid with parallel sides AB > CD. Points K and L lie on the line segments AB and CD, respectively, so that \frac {AK}{KB} = \frac {DL}{LC}. Suppose that there are points P and Q on the line segment KL satisfying \angle{APB} = \angle{BCD} and \angle{CQD} = \angle{ABC}. Prove that the points P, Q, B and C are concylic.
Izvor: Međunarodna matematička olimpijada, shortlist 2006