Cevian conjugate | conjugate points

The isotomic conjugate of a point is the point of concurrence Q of the isotomic lines relative to a point P. The isotomic conjugate α' :β' :γ' of a point with trilinear coordinates α:β:γ is (a^2 α)^(-1) :(b^2 β)^(-1) :(c^2 γ)^(-1). Vandeghen calls the transformation taking points to their isotomic conjugates the Cevian transform. The product of isotomic and isogonal is a collineation which transforms the sides of a triangle to themselves. An isotomic transversal is sometimes referred to as an isotomic conjugate (Ehrmann and van Lamoen 2004).

Cevian transform | Gergonne point | isogonal conjugate | isotomic lines | isotomic transform | isotomic transversal | Jerabek hyperbola | Nagel point | Steiner circumellipse