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IMO Shortlist 2013, Geometry #5

Source: IMO Shortlist 2013, Geometry #5

July 10, 2014
geometrycomplex numbershexagonIMO Shortlist

Problem Statement

Let ABCDEFABCDEF be a convex hexagon with AB=DEAB=DE, BC=EFBC=EF, CD=FACD=FA, and ∠A−∠D=∠C−∠F=∠E−∠B\angle A-\angle D = \angle C -\angle F = \angle E -\angle B. Prove that the diagonals ADAD, BEBE, and CFCF are concurrent.
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