A Cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension). The condition for three general Cevians from the three vertices of a triangle to concur is known as Ceva's theorem. Picking a Cevian point P in the interior of a triangle Δ A B C and drawing Cevians from each vertex through P to the opposite side produces a set of three intersecting Cevians A A', B B', and C C' with respect to that point. The triangle Δ A' B' C' is known as the Cevian triangle of Δ A B C with respect to P, and the circumcircle of Δ A' B' C' is similarly known as the Cevian circle.

angle bisector | Ceva's theorem | Cevian circle | Cevian point | Cevian triangle | pedal-Cevian point | Routh's theorem | splitter | triangle median