Among the conics defined in this way there is a prominent one for which the above points coincide with the projections of the excenters D, E, F of triangle ABC. In this case the radius r = s = (a+b+c)/2 is the semi-perimeter of the triangle.

The proof is a consequence of the discussion made in EqualCirclesAtVertices.html . Regarding the special conic referred above see the reference below on the

EqualCirclesAtVertices.html

Menelaus.html

Mittenpunkt.html

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