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locus of the midpoints of the sides KL for all equilaterals KLM

Source: 2022 Argentina OMA Finals L3 p3

November 14, 2022
geometryLocusEquilateralmidpoint

Problem Statement

Given a square ABCDABCD, let us consider an equilateral triangle KLMKLM, whose vertices KK, LL and MM belong to the sides ABAB, BCBC and CDCD respectively. Find the locus of the midpoints of the sides KLKL for all possible equilateral triangles KLMKLM.
Note: The set of points that satisfy a property is called a locus.
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