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locus of point on triangle

Source: Mongolia 1999 Grade 10 P6

May 5, 2021
geometry

Problem Statement

A point MM lies on the side ACAC of a triangle ABCABC. The circle γ\gamma with the diameter BMBM intersects the lines ABAB and BCBC at PP and QQ, respectively. Find the locus of the intersection point of the tangents to γ\gamma at PP and QQ when point MM varies.