Ceva's theorem

Simple yet powerful theorem that gives the properties of concurrent lines from vertices in a triangle is Ceva's theorem. If the lines AD, BE and CF are concurrent, then  AF/FB x BD/CD x CE/EA = 1. This is attributed to Italina mathematician Giovanni Ceva.

The lines that start from vertices to opposite edges are called cevians. Some examples are medians, angle bisectors, altitudes. Theorem can be used to easily determine whether three such lines are concurrent. Intersection points of such lines are significant centers of triangle in geometry. Some example centers of triangle are centroid, incenter, circumcenter and orthocenter.

References
* Ceva's theorem
* Ceva's theorem
* Triangle Centers