How do you solve this? (Picture included)?

Question

This is from an SAT subject test (Math 2) online prep. I can't figure it out for the life of me! Please don't just tell me the answer, but also how you're supposed to figure it out!

http://i223.photobucket.com/albums/dd205/OkayThanksToYou/SATquestion.jpg

Thanks so much!! I'll pick a best answer TONIGHT!

Answer 1

answer length of line ab = 3.63

since those lines at 50 degrees are tangential the points where they touch the circle if connect to the center of the circle will form a rt angle.

I solved it using trigonometry and laws of similar triangles. It looks like a kite so I cut it in 2. I viewed an angle 25 degrees, 65 degrees and 90 degrees with one side of 2.

Finally I took one line from the center to the tangent point with a length of 2. I took the cosine of 65 degrees and got .9063

Opp / hyp so 1/2 AB = opp

opp / 2 = .9063 so opp = .18126 so times 2 = 0.36252 0r 0.363 close enough

Answer 2

well the first thing u do is draw a line from A to B

now u have a complete triangle

C A B
a triangle now has 3 sides with angles
50 degs + 65 degs + 65 degs

now
take the 2in radius and point to A
and do the same for B

now
u have another triangle


A, B, and (center of radius 2in)

now i will try and draw it

C
/\
/ \
/ \
/ \
/ \
----------
\ /
\ /
\ /
\ /
\ /
\ /

do u see it now
try to fiqure it out
email me for more help

Answer 3

O center --> and OA=OB=r=2

Like ACB=50º --> OCB=25º --> COB=90º-25º=65º
--> sin65º=h/2= (AB/2)/2 = AB/4 --> AB=4·sin65º
--> 3,6252.... ~ 3,63 d)

Saludos.