The Brocard inellipse is the inconic with parameters x:y:z = 1/a :1/b :1/c, giving the trilinear equation α^2/a^2 + β^2/b^2 + γ^2/c^2 - (2αβ)/(a b) - (2αγ)/(a c) - (2βγ)/(b c) = 0. It has the Brocard points Ω and Ω' of a triangle as its foci and the Brocard midpoint as its center. Its Brianchon point is the symmedian point K of the triangle, and the triangle formed by the points of contact of the inellipse with the reference triangle is the symmedial triangle, which is also its polar triangle.

inconic | inellipse | symmedial triangle | symmedian point

Pierre René Jean Baptiste Henri Brocard