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MMO 325 Moscow MO 1956 locus of midpoints, equal segments related

Source:

August 19, 2019
geometryequal segmentsmidpointLocus

Problem Statement

On sides ABAB and CBCB of ABC\vartriangle ABC there are drawn equal segments, ADAD and CECE, respectively, of arbitrary length (but shorter than min(AB,BCAB,BC)). Find the locus of midpoints of all possible segments DEDE.