MEMO 2012 ekipno problem 6


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June 23, 2013
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Let ABCD be a convex quadrilateral with no pair of parallel sides, such that \angle ABC  = \angle CDA. Assume that the intersections of the pairs of neighbouring angle bisectors of ABCD form a convex quadrilateral EFGH. Let K be the intersection of the diagonals of EFGH. Prove that the lines AB and CD intersect on the circumcircle of the triangle BKD.
Source: Srednjoeuropska matematička olimpijada 2012, ekipno natjecanje, problem 6