EqualCirclesConic

Equal circles conics

Consider a triangle ABC and draw three equal circles with radius (r) centered at its vertices. The intersection points of the circles with the sides of ABC define six points G, H, I, J, K, L lying on a conic.
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 Mittenpunkt.

Equal circles conics

See Also