The inconic having inconic parameters x:y:z = a/(b + c - a) :b/(a + c - b) :c/(a + b - c). Its center is the mittenpunkt M of the triangle and its Brianchon point is the Nagel point Na. The Mandart ellipse touches the sides of the triangle in the vertices of the extouch triangle, which is also its polar triangle. It has area A = π((a + b - c)(b + c - a)(c + a - b))/[2(a b + b c + c a) - (a^2 + b^2 + c^2)]^(3/2) Δ, where Δ is the area of the reference triangle.

Brianchon point | extouch triangle | inconic