Given a point P and a triangle Δ A B C, the Cevian triangle Δ A' B' C' is defined as the triangle composed of the endpoints of the cevians though the Cevian point P. A triangle and its Cevian triangle are therefore perspective with respect to the Cevian point. If the point P has trilinear coordinates α:β:γ, then the Cevian triangle has trilinear vertex matrix [0 | β | γ α | 0 | γ α | β | 0] (Kimberling 1998, pp. 55 and 185), and is a central triangle of type 1.
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