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equilateral triangles build on sides of a quadrilateral

Source: Moldova TST, day 1, problem 3

March 8, 2011
geometrygeometric transformationrotationvectorgeometry unsolved

Problem Statement

Let ABCDABCD be a quadrilateral and MM the midpoint of the segment ABAB. Outside of the quadrilateral are constructed the equilateral triangles BCEBCE, CDFCDF and DAGDAG. Let PP and NN be the midpoints of the segments GFGF and EFEF. Prove that the triangle MNPMNP is equilateral.
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