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Hexagon ABCDEF: 2011 USAMO #3

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April 28, 2011
AMCUSA(J)MOUSAMOgeometrygeometric transformationreflection3D geometry

Problem Statement

In hexagon ABCDEFABCDEF, which is nonconvex but not self-intersecting, no pair of opposite sides are parallel. The internal angles satisfy ∠A=3∠D\angle A=3\angle D, ∠C=3∠F\angle C=3\angle F, and ∠E=3∠B\angle E=3\angle B. Furthermore AB=DEAB=DE, BC=EFBC=EF, and CD=FACD=FA. Prove that diagonals AD‾\overline{AD}, BE‾\overline{BE}, and CF‾\overline{CF} are concurrent.
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