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min sum of distances of a point of circle from equidistant points from center

Source: 2012 Oral Moscow Geometry Olympiad grades 10-11 p5

September 25, 2019
minimumSumdistancegeometrycircle

Problem Statement

Inside the circle with center OO, points AA and BB are marked so that OA=OBOA = OB. Draw a point MM on the circle from which the sum of the distances to points AA and BB is the smallest among all possible.
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