The basic properties of the maximal triangles inscribed in (e) are discussed in MaximalTrianglesInEllipse.html . The statement on the ellipse (f) follows from an easy calculation. That on (g) follows from the well known relation MH = 2*OM on the Euler line OH. M is the centroid of all maximal triangles. The radius r of the circle (h) can be calculated and the product PM*MQ = (r+OM)*(r-OM) gives the formula after a calculation. Steiner goes further in the cited reference and gives the maximum and minimum values of the radius r=r(A) and the corresponding product p = p(A)=AB*BC*CA of sides of the triangle:

Look at the file CircumcentersLocus.html for the story of the shape and a parametrization of the locus of circumcenters O.

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