2011 USAMO Problems/Problem 3

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

2011 USAMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
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2011 USAMO Problems/Problem 3

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