Question #N842
A circle with radius 5 has a chord of length 8. What is the distance, in units, from the center of the circle to the midpoint of the chord?
A. 2
B. 3
C. 4
D. 5
Correct Answer is: B
A chord of a circle and the radius drawn to the midpoint of the chord form a right triangle. The radius is the hypotenuse of this triangle. The midpoint of the chord divides the chord into two equal segments of length 4. Therefore, the distance from the center of the circle to the midpoint of the chord is one leg of a right triangle with hypotenuse of length 5 and the other leg of length 4. Using the Pythagorean Theorem, we have or . Therefore, the distance is 3.