# Cevian line

From Citizendium

In triangle geometry, a **Cevian line** is a line in a triangle joining a vertex of the triangle to a point on the opposite side. A **Cevian set** is a set of three lines lines, one for each vertex. A Cevian set is **concurrent** if the three lines meet in a single point.

## Ceva's theorem

Let the triangle be *ABC*, with the Cevian lines being *AX*, *BY* and *CZ*. **Ceva's theorem** states that the Cevian set is concurrent if and only if

## Concurrent sets

Examples of concurrent Cevian sets include:

- The altitudes, meeting at the orthocentre
- The medians, meeting at the centroid
- The angle bisectors, meeting at the incentre

## References

- H.S.M. Coxeter; S.L. Greitzer (1967).
*Geometry revisited*. MAA. ISBN 0-88385-619-0.