Cevian

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:
  \(b^{2}m+c^{2}n = a(d^{2}+mn)\)

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