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.

 Aug 13, 2018

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





cool cool cool

 Aug 13, 2018

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