+64 In triangle ABC, AB=9, BC=12, AC=15, and CD is the angle bisector. Find the length of CD.
+129852
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 :
