Problem: AB is a diameter of a circle centered at O.C is a point on the circle such that angle BOC is 60∘. If the diameter of the circle is 5 inches, the length of chord AC, expressed in inches, is:
Answer Choices:
A. 3
B. 252
C. 253
D. 33
E. none of these
Solution:
Triangle ABC is a right triangle with hypotenuse AB=5 inches and leg BC equal to a radius of the circle, 25. We, therefore, have AC2=AB2−BC2=25−425=475∴AC=253 (inches).