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MEF equilateral if ABC equilateral, CD = CE, DMFB #

Source: Netherlands - Dutch NMO 1981 p2

January 28, 2023
Equilateralgeometry

Problem Statement

Given is the equilateral triangle ABCABC with center MM. On CACA and CBCB the respective points DD and EE lie such that CD=CECD = CE. FF is such that DMFBDMFB is a parallelogram. Prove that △MEF\vartriangle MEF is equilateral.
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