Question

Suppose a radius of a circle is 17 units and a chord is 30 units long. Find the distance from the center of

the circle to the chord.

Answer 1

Let A represent the center of the circle. Let the point B be a point at the intersection of the one end of the chord and the edge of the circle. Finally, let C represent a point between the center of the circle and the midpoint of the cord. The triangle ABC is a right triangle with a 90 degree angle at ACB. Since the cord length is 30, the bisected segment BC is length 15 .

(length AB)^2 = (length BC)^2 + (length AC)^2

17^2 = 15^2 + (length AC)^2

289 = 225 + (length AC)^2

add -225 to each side

64 = (length AC)^2

take square root of each side

8 = length AC