Geometry · Areas of triangles · Centroid · Locus problems · Anticomplementary triangle · Convex position · Case analysis
A triangle \(ABC\) is given. Find every point \(M\) of its plane for which the three triangles \(ABM\), \(BCM\) and \(CAM\) have equal areas.
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Serbian Republic Competition (Republicko takmicenje) 1998, high school grade I, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source