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locus of midpoints, equilateral triangles related

Source: 1999 Estonia National Olympiad Final Round grade 10 p5

March 11, 2020
geometryLocusmidpointEquilateral

Problem Statement

Let CC be an interior point of line segment ABAB. Equilateral triangles ADCADC and CEBCEB are constructed to the same side from ABAB. Find all points which can be the midpoint of the segment DEDE.
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