The de Longchamps circle is defined as the radical circle of the power circles of a given reference triangle. It is defined only for obtuse triangles. It is the complement of the polar circle. It has circle function l = - a^2/(b c), corresponding to Kimberling center X_32. Its center is the de Longchamps point L (X_20), and its radius is R_L = 4Rsqrt(-cos A cos B cos C), where R is the circumradius of the reference triangle.

de Longchamps ellipse | orthogonal circles | power circles | radical circle