Cevian

[1][2] Medians and angle bisectors are special cases of cevians.

[3] The length of a cevian can be determined by Stewart's theorem: in the diagram, the cevian length d is given by the formula Less commonly, this is also represented (with some rearrangement) by the following mnemonic: If the cevian happens to be a median (thus bisecting a side), its length can be determined from the formula or since Hence in this case If the cevian happens to be an angle bisector, its length obeys the formulas and[5] and where the semiperimeter

There are various properties of the ratios of lengths formed by three cevians all passing through the same arbitrary interior point:[6]: 177–188  Referring to the diagram at right, The first property is known as Ceva's theorem.

Three of the area bisectors of a triangle are its medians, which connect the vertices to the opposite side midpoints.

Thus a uniform-density triangle would in principle balance on a razor supporting any of the medians.