Suppose be is an angle bisector of △abc, ab=9, bc=15, and ac=16. find ae and ec.

AE=5 and EC=10

Step-by-step explanation:

Given : Suppose BE is an angle bisector of ΔABC , AB=9, BC=15, and AC=16

To find : AE and EC

Solution : BE form an angle bisector on line AC

Let AE=x and EC = y

Length of AC= AE+EC , putting values

16=x+y .....[1]

Now, we apply angle bisecor theorem which state that the ratio of the length of the line segment AE to the length of segment EC is equal to the ratio of the length of side AB to the length of side AC

Put values,

Cross multiply,

.......[2]

From [1] and [2]

Substitute x from [1] in [2], x= 16-y

Put y in value of x,

x= 16-y

x=16-10=6

Therefore, length of AE=x=5 and EC=y=10

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

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