Ceva's theorem

Named after Italian mathematician Giovanni Ceva (1647-1734), to whom the discovery of the theorem is often attributed.

Ceva's theorem

1. (mathematics) A theorem about triangles in plane geometry, regards the ratio of the side lengths of a triangle divided by cevians.

In mathematical terms, the theorem states: let D, E, and F, be points on the sides BC, CA, and AB of a triangle (possibly extended). Then AD, BE, and CF are concurrent if and only if ${\displaystyle {\frac {AF}{FB}}\cdot {\frac {BD}{DC}}\cdot {\frac {CE}{EA}}=1.}$