The symmedial triangle Δ K_A K_B K_C (a term coined here for the first time), is the triangle whose vertices are the intersection points of the symmedians with the reference triangle Δ A B C. It has the very simple trilinear vertex matrix [0 | b | c a | 0 | c a | b | 0]. It is by definition perspective with the reference triangle, with perspector given by the symmedian point K. It is the cyclocevian triangle with respect to Kimberling center X_1031. The symmedial triangle is the polar triangle of the Brocard inellipse.

Brocard inellipse | symmedial circle | symmedian | symmedian point