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Middle European Mathematical Olympiad 2012 - Team Compt. T-6

Source: Middle European Mathematical Olympiad 2012 - Team Compt. T-6

September 14, 2012
geometrycircumcircletrapezoidincenterangle bisectorgeometry proposed

Problem Statement

Let ABCD ABCD be a convex quadrilateral with no pair of parallel sides, such that ∠ABC=∠CDA \angle ABC = \angle CDA . Assume that the intersections of the pairs of neighbouring angle bisectors of ABCD ABCD form a convex quadrilateral EFGH EFGH . Let K K be the intersection of the diagonals of EFGH EFGH. Prove that the lines AB AB and CD CD intersect on the circumcircle of the triangle BKD BKD .
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