SOLUTION: Circle O has a radius of 12. Points A and B are on the circle forming radii OA and OB. What is the length of line AB if measure of angle AOB = 120? The answer is 12 square root

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Question 1110559: Circle O has a radius of 12. Points A and B are on the circle forming radii OA and OB. What is the length of line AB if measure of angle AOB = 120?
The answer is 12 square root of 3
Can somebody explain to me how to get to the answer.
Thanks!
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Triangle AOB is isosceles, because AO and OB are radii of the circle.

Let C be the point on AB such that OC is the perpendicular bisector of AB.

Then triangles AOC and BOC are 30-60-90 right triangles, with OC the short leg.

That means OC=6; then AC = BC = 6*sqrt(3), so AB = 12*sqrt(3).