Question #N240

A circle has a radius of 5 units. A chord of the circle is 8 units long. What is the distance, in units, from the center of the circle to the chord?
A. 2
B. 3
C. 4
D. 6

Correct Answer is: B

Draw a diagram of the circle with the chord and the radii to the endpoints of the chord. This creates an isosceles triangle where the chord is the base and the two radii are the legs. The distance from the center of the circle to the chord is the height of this triangle. Since the triangle is isosceles, the height bisects the base, making two right triangles with legs of length 4 units and a hypotenuse of length 5 units. Using the Pythagorean theorem, the height of the triangle is 3 units, which is the distance from the center of the circle to the chord.