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F D =FM wanted , AB=BC, equilateral BCD

Source: 2020 Dutch BxMO TST p4

November 21, 2020
equal segmentsEquilateralgeometry

Problem Statement

Three different points A,BA,B and CC lie on a circle with center MM so that ∣AB∣=∣BC∣| AB | = | BC |. Point DD is inside the circle in such a way that △BCD\vartriangle BCD is equilateral. Let FF be the second intersection of ADAD with the circle . Prove that ∣FD∣=∣FM∣| F D | = | FM |.
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