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locus of points M so BM x CM / MA_1 is minimal, A_1 = AM \cap (ABC)

Source: Moldova 2002 TST 3 P3

August 25, 2018
geometryLocusminimum

Problem Statement

A triangle ABCABC is inscribed in a circle GG. For any point MM inside the triangle, A1A_1 denotes the intersection of the ray AMAM with GG. Find the locus of point MM for which BM⋅CMMA1\frac{BM\cdot CM}{MA_1} is minimal, and find this minimum value.
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