Question #N294

In a circle with a radius of 5, a chord is drawn that is 8 units long. What is the distance from the center of the circle to the chord?
A. 2
B. 3
C. 4
D. 5

Correct Answer is: B

Draw a radius from the center of the circle to an endpoint of the chord, and draw another radius to the other endpoint of the chord. This creates an isosceles triangle with the chord as its base and the two radii as its legs. The altitude from the center of the circle to the chord bisects the chord, creating two right triangles. Each of these right triangles has a hypotenuse of 5 and a leg of 4. Using the Pythagorean Theorem, we can find the length of the other leg, which is the distance from the center of the circle to the chord: $\sqrt{5^2 - 4^2} = \sqrt{9} = 3$.