Question

11. Use the above figure to answer the question. How long is arc ACB if the radius of the circle is 6? Round your answer to two decimal places. A. 25.13 B. 18.86 C. 6.29 D. 12.57

Answer 1

I have to assume that figures OAT and OBT are congruent.

If that is true, the center angle O (of the sector AOB= is 120° and the angle of the sector ACB is 360° - 120° = 240°

Now you can state that the circumferece of the circle / 360 ° = arc ACB / 240° and solve for arc ACB.

arc ACB = circumference * 240 / 360 = 2πr *240/360 = 2π(6)*240/360 = 25.13

Answer: option A. 25.13