Question #N1015

A circle with center $O$ has a radius of 5. Point $A$ lies on the circle, and line segment $OA$ is a diameter of the circle. If point $B$ lies on the circle such that angle $AOB$ measures 120 degrees, what is the length of line segment $AB$?
A. 5
B. 5\sqrt{2}
C. 5\sqrt{3}
D. 10

Correct Answer is: C

Triangle $AOB$ is an equilateral triangle because it has two sides that are radii of the circle and a 120-degree angle. The length of side $AB$ is equal to the radius of the circle, which is 5. Since triangle $AOB$ is equilateral, the length of side $AB$ is also equal to 5. Therefore, the length of line segment $AB$ is $5\sqrt{3}$.