Given a point P, the lines AP, BP and CP cut the opposite sides of the triangle ABC at A', B', C'. Then the triangle A'B'C' is the cevian triangle of P. Its vertices A', B' and C' are called the cevian traces (or simply the traces) of P.
As example:
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 incenter is the incentric triangle.
The cevian triangle of the Gergonne point is the intouch triangle.
The cevian triangle of the Nagel point is the extouch triangle.