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Locus of points whose area of pedal triangle is constant

Source: Vietnam MO 1983 P3

March 18, 2011
geometrygeometry proposed

Problem Statement

A triangle ABCABC and a positive number kk are given. Find the locus of a point MM inside the triangle such that the projections of MM on the sides of ΔABC\Delta ABC form a triangle of area kk.
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