A chord is 16 units from the center of a circle. The radius of the circle is 20 units. What is the length of the chord?

Answer 1

Draw a line from the center of the circle to the chord to form a right triangle.

The radius (20) forms the hypotenuse of the right triangle and distance from the center to the chord (16) forms a leg.

Use the Pythagorean Theorem to find the length of the other leg x (which would be 1/2 the length of the chord):

x^2 + 16^2 = 20^

x = 12

So the entire chord length = 12 * 2 = 24 units

Answer 2

Let AB be our chord. ^2

O - is the center of the circle. Let OC be the distance 16. Which means OA = OB = 20 (radius). Since OC is perpendicular to AB and AC = CB by the property of a chord,

2*AC = AB.

AO^2 = AC^2 + OC^2 - RIGHT TRIANGLE

AC = sqrt (AO^2 - OC^2 )

OA = 20

OC = 16

=> AB = 2 * sqrt ( 20^2 - 16^2) = 2 * sqrt (144) = 2* 12 = 24