Cevian

Line segment joining the vertex of a triangle to its opposite side.

Properties

In triangles, altitudes, medians and angle bisectors are special types of cevians.

The length of a cevian can be determined by using the formula: [latex]b^{2}m+c^{2}n = a(d^{2}+mn)[/latex]

cevienne

If the cevian is an altitude, its length is given by the formula: [latex]d^{2}=b^{2}-n^{2}=c^{2}-m^{2}[/latex].
If the cevian is a median, its length is given by the formula: [latex]m(b^{2}+c^{2})=a(d^{2}+m^{2})[/latex].
If the cevian is a bisector, its length is given by the formula: [latex]{(b+c)}^{2}=a^{2}(\frac{d^{2}}{mn}+1)[/latex].

Historical Note

The term cervian is named for Italian mathematician Giovanni Ceva, who proved a theorem about cevians that also bears his name.