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 In triangle ABC, AB=9, BC=12, AC=15, and CD is the angle bisector. Find the length of CD.

bbelt711  Jul 25, 2017
 #1
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+1

 

CD will establish the following relationship

 

AD / BD = AC /BC

 

So......

 

AD/BD = 15/12= 5/4

 

Therefore....BD  = (4/9)9  =  4

 

And by the Pythagorean Theorem,

 

CD  =  sqrt (BD^2 + BC^2) = sqrt ( 4^2 + 12^2 )  = sqrt ( 16 + 144)  = sqrt (160)  = 4sqrt(10)  units ≈ 12.65 units

 

Here's a pic :

 

 

 

cool cool cool

CPhill  Jul 25, 2017
edited by CPhill  Jul 25, 2017

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