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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
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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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