IMO Shortlist 2008 problem G2


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2. travnja 2012.
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Given trapezoid ABCD with parallel sides AB and CD, assume that there exist points E on line BC outside segment BC, and F inside segment AD such that \angle DAE = \angle CBF. Denote by I the point of intersection of CD and EF, and by J the point of intersection of AB and EF. Let K be the midpoint of segment EF, assume it does not lie on line AB. Prove that I belongs to the circumcircle of ABK if and only if K belongs to the circumcircle of CDJ.

Proposed by Charles Leytem, Luxembourg
Izvor: Međunarodna matematička olimpijada, shortlist 2008