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?

- anonymous

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- jamiebookeater

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- anonymous

It uses this picture

- vishal_kothari

wait for a minute...

- anonymous

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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## More answers

- vishal_kothari

C.

- anonymous

Can you explain how?

- vishal_kothari

in which grade you are in?

- anonymous

8th, but I'm taking Geometry.

- vishal_kothari

the concept i used is taught in 11th grade...

- anonymous

Try me

- vishal_kothari

what?

- anonymous

As in, let's see if I can understand it.

- vishal_kothari

in AFE,
tan60=AE/AF
\[\sqrt{3}\]=12/AF
AF=4\[\sqrt{3}\]

- anonymous

whoops, sorry

- vishal_kothari

why you are sorry...

- anonymous

because I accidentally typed a phrase that was incongruous in our conversation?

- anonymous

oh well

- vishal_kothari

u in which country...

- anonymous

America?

- anonymous

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

- vishal_kothari

i also used that...

- anonymous

ok

- anonymous

well i understand how AF = 4(sqrt 3)

- anonymous

what im not getting is how to solve for DF

- vishal_kothari

really...

- vishal_kothari

u understand how to get AF..

- anonymous

well, i didn't understand how u explained it, but i did arrive at the same answer - 4(sqrt 3)

- anonymous

so let's see - if we use 30-60-90 triangles as our basis, then DF = 2CF, correct?

- vishal_kothari

if i will give you the value of CF.. THAN COULD U FIND DF...

- vishal_kothari

CF=AC-AF=12-4\[\sqrt{3}\]

- anonymous

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) =

- anonymous

yeah ok good, we agree so far

- anonymous

so 12 - 4(sqrt 3) = 5.07179677

- anonymous

Using 30-60-90 Triangles, DF is 2x this, or 10.1435935

- vishal_kothari

YA..

- vishal_kothari

ARE U AT FACEBOOK...

- anonymous

no

- anonymous

okay

- anonymous

good, thank you for your time

- vishal_kothari

WELCOME

- anonymous

so i am new to this website - how do i thank you in return?

- vishal_kothari

IT'S 12:25 A.M. HERE..

- anonymous

oh sorry

- anonymous

why are you using a computer at 12:30?

- anonymous

oh well

- anonymous

so do i thank you by clicking good answer on all of your responses?

- vishal_kothari

YOUR WISH..

- anonymous

i told you im new - im not sure what to do now

- vishal_kothari

WELL IT WAS MY BROTHER'S BIRTHDAY .....SO 12:30..

- vishal_kothari

GIVE ME A MEDAL AND YOUR LEVEL WILL INCREASE..

- anonymous

can i give u multiple if i feel like it?

- anonymous

oh w8, other people have to

- anonymous

all right, thank you again for all your help

- vishal_kothari

WELCOME

- vishal_kothari

ASK MORE QUESTIONS IF YOU HAVE ...

- anonymous

I'm fine for now, but I definitely will when I have another one.

- vishal_kothari

OK

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