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Part of 1981 Dutch Mathematical Olympiad

Problems(1)

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

Source: Netherlands - Dutch NMO 1981 p2

1/28/2023
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.
Equilateralgeometry