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AC // BK wanted, equilaterals ABC and MKC

Source: 2009 Moldova NMO 9.3

March 27, 2021
geometryEquilateralparallel

Problem Statement

Let ABCABC be an equilateral triangle. The points MM and KK are located in different half-planes with respect to line BCBC, so that the point M∈(AB)M \in (AB) ¸and the triangle MKCMKC is equilateral. Prove that the lines ACAC and BKBK are parallel.
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