In triangle ABC we have that AB=AC=14 and BC=26. What is the length of the shortest angle bisector in ABC? Express your answer in simplest radical form.

anomy Aug 13, 2018

#1**+1 **

This triangle is isoceles.....the shortest angle bisector will be the one that bisescts angle "A"....it will be the altitude of the triangle

We can find the length of this bisector using the Pythagorean Theorem

Length = √ [ 14^2 - 13^2 ] = √ [196 - 169 ] = √27 = 3√3 units

Here's a pic with AD, BE and CF being the bisectors.....as you can see, AD is the shortest bisector

CPhill Aug 13, 2018