Question 1087690
AB = c = 9
BC = a = 12
AC = b = 15
Let CD be d, this is the length of this bisector.
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Length of angle bisector theorem:
d^2 = [ab/(a+b)^2]((a+b)^2-c^2)
where a, b, and c are the sides opposite A, B and C respectively. 
Substitute with your numbers:
d^2 = [(12(15))/(12+15)^2]((12+15)^2-9^2) use your calculator and you get:
d^2 = 160 
take the square root on both sides:
d = 12.65
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Did you draw it? I did, it's the first thing you should do whenever possible.
*[illustration a_length_bisector.JPG]