area of the whole tringle = sum of the two triangles produced by the bisector. let the length of the bisector is L.then 1/2 Lcsin A/2 + 1/2 LbsinA/2 = 1/2 bc sin Athen 1/2 Lcsin A/2 + 1/2 LbsinA/2 = 1/2 bc 2sin A/2 cos A/2 from which L = 2bc cosA/2 / (b+c)
