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TOT 273 1990 Autumn A S2 equailateral givena and wanted

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June 8, 2024
geometryEquilateralequilaterals

Problem Statement

A point MM is chosen on the arc ACAC of the circumcircle of the equilateral triangle ABCABC. PP is the midpoint of this arc, NN is the midpoint of the chord BMBM and KK is the foot of the perpendicular drawn from PP to MCMC. Prove that the triangle ANKANK is equilateral.
(I Nagel, Yevpatoria)
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