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How to find the Fermat Point using the construction of the tangent to ellipse?

Be done the triangle ABC, it is known the method to finding the point Q that minimises the sum QA+QB+QC among all points Q in the plane (The Fermat point). I want a hint for solving this problem using the construction of the tangent to ellipse. (Hadamard, Lesson de Geometrie Elementaire, II, problem no. 745).