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We have a triangle ABC such that AB=6, BC=8,  and CA=10 If AD is an angle bisector such that D is on BC,  then find the value of AD^2.

 Jul 9, 2021
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A

 

6                  10

 

B            8                   C

 

This  is a 6 - 8 -10    right  triange

 

Since  AD is  an angle  bisector   we have  that

 

AD / DC  =   AB  / AC

 

AD /DC  =  6 / 10

 

AD/ DC  = 3/5

 

AD  =  3/ ( 3 + 5)  * 8     =   (3/8) (8) =  3

 

AD^2  =  3^2   =   9  

 

 

cool cool cool

 Jul 9, 2021
edited by CPhill  Jul 9, 2021

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