Geometry · Locus · Thales circle · Angle side inequality · Exterior angle theorem · Monotone distance
Two fixed points \(A\) and \(B\) are given in the plane. A point \(M\) is chosen and then travels along the straight segment from \(M\) to \(A\). Determine all positions of \(M\) for which the distance to \(B\) increases the whole way, that is, for which the distance from \(B\) to the travelling point is strictly larger at every later moment than at every earlier one.
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Serbian Republic Competition (Republicko takmicenje) 1997, high school grade I, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source