Question #N793
A circle with center $O$ has a radius of 5. Point $A$ lies on the circle, and the measure of angle $AOB$ is 60 degrees. What is the length of chord $AB$?
A. 5
B. 10
C. 5\sqrt{3}
D. 10\sqrt{3}
Correct Answer is: C
Angle $AOB$ is a central angle of the circle, so triangle $AOB$ is an equilateral triangle. Therefore, chord $AB$ has the same length as the radius of the circle, 5. The height of triangle $AOB$ is $5\sqrt{3}$, and this is also the length of the altitude from point $O$ to chord $AB$, which divides chord $AB$ into two congruent segments. Since the altitude bisects chord $AB$, the length of chord $AB$ is $2(5\sqrt{3}) = 5\sqrt{3}$.