The antipedal triangle Δ A' B' C' of a reference triangle Δ A B C with respect to a given point P is the triangle of which Δ A B C is the pedal triangle with respect to P. If the point P has trilinear coordinates α:β:γ and the angles of Δ A B C are A, B, and C, then the antipedal triangle has trilinear vertex matrix [-(β + α cos C)(γ + α cos B) | (γ + α cos B)(α + β cos C) | (β + α cos C)(α + γ cos B) (γ + β cos A)(β + α cos C) | -(γ + β cos A)(α + β cos C) | (α + β cos C)(β + γ cos A) (β + γ cos A)(γ + α cos B) | (α + γ cos B)(γ + β cos A) | -(α + γ cos B)(β + γ cos A)] (Kimberling 1998, p. 187). The antipedal triangle is a central triangle of type 2.

antipedal line | pedal triangle