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Polish 2nd stage 2010, 4th problem (pentagon with one angle)

Source:

November 11, 2010
geometryincenterperpendicular bisectorangle bisectorgeometry proposed

Problem Statement

In the convex pentagon ABCDEABCDE all interior angles have the same measure. Prove that the perpendicular bisector of segment EAEA, the perpendicular bisector of segment BCBC and the angle bisector of ∠CDE\angle CDE intersect in one point.
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