Cevian Triangle

Let P be a point not on a sideline of

ABC. The cevian triangle of P with respect to

ABC is the triangle whose vertices are the endpoints of the cevians of P.

A₁B₁C₁ - cevian triangle of P.

Examples:

The cevian triangle of the Incenter is the Incentral Triangle.
The cevian triangle of the Centroid is the Medial Triangle.
The cevian triangle of the Orthocenter is the Orthic Triangle.
The cevian triangle of the Symmedian Point is the Symmedial Triangle.
The cevian triangle of the Gergonne point is the Intouch Triangle.
The cevian triangle of the Nagel point is the Extouch Triangle.