CD is tangent to the circle and segment AE is perpendicular to segment AC. If a radius of the circle measures 12 in., which is the value of DF + AF?

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CD is tangent to the circle and segment AE is perpendicular to segment AC. If a radius of the circle measures 12 in., which is the value of DF + AF?

Mathematics
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It's multiple choice; these are the answers given: A. 28 + 5(sqrt 3) B. 28 - 4(sqrt 3) C. 24 - 4(sqrt 3) D. 21 + 2(sqrt 3)

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Other answers:

C.
Can you explain how?
in which grade you are in?
8th, but I'm taking Geometry.
the concept i used is taught in 11th grade...
Try me
what?
As in, let's see if I can understand it.
in AFE, tan60=AE/AF \[\sqrt{3}\]=12/AF AF=4\[\sqrt{3}\]
whoops, sorry
why you are sorry...
because I accidentally typed a phrase that was incongruous in our conversation?
oh well
u in which country...
America?
This question was posed to me in my geometry class - are u sure there's no easier way to solve it? I was thinking something to do with 30-60-90 triangles
i also used that...
ok
well i understand how AF = 4(sqrt 3)
what im not getting is how to solve for DF
really...
u understand how to get AF..
well, i didn't understand how u explained it, but i did arrive at the same answer - 4(sqrt 3)
so let's see - if we use 30-60-90 triangles as our basis, then DF = 2CF, correct?
if i will give you the value of CF.. THAN COULD U FIND DF...
CF=AC-AF=12-4\[\sqrt{3}\]
I think I could, but what I'm getting is not 24, like you say it is. That's why I'm going to show you how I would solve it, and I ask that you please correct me if I am wrong. AC = 12, because it is a radius. We have determined that AF = 4(sqrt 3). 12 - 4(sqrt 3) =
yeah ok good, we agree so far
so 12 - 4(sqrt 3) = 5.07179677
Using 30-60-90 Triangles, DF is 2x this, or 10.1435935
YA..
ARE U AT FACEBOOK...
no
okay
good, thank you for your time
WELCOME
so i am new to this website - how do i thank you in return?
IT'S 12:25 A.M. HERE..
oh sorry
why are you using a computer at 12:30?
oh well
so do i thank you by clicking good answer on all of your responses?
YOUR WISH..
i told you im new - im not sure what to do now
WELL IT WAS MY BROTHER'S BIRTHDAY .....SO 12:30..
GIVE ME A MEDAL AND YOUR LEVEL WILL INCREASE..
can i give u multiple if i feel like it?
oh w8, other people have to
all right, thank you again for all your help
WELCOME
ASK MORE QUESTIONS IF YOU HAVE ...
I'm fine for now, but I definitely will when I have another one.
OK

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