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ASU 420 All Soviet Union MO 1986 min area of circle's intersection

Source:

August 5, 2019
geometryareasminimumcircles

Problem Statement

The point MM belongs to the side [AC][AC] of the acute-angle triangle ABCABC. Two circles are circumscribed around triangles ABMABM and BCMBCM . What MM position corresponds to the minimal area of those circles intersection?
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