Question

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?

How is the measure of a central angle and the corresponding chord related to the measure of the arc intercepted by the chord?

Answer 1

Length of the chord: 24 units

Angles are equal

Explanation:

Drop a Perpendicular from the centre onto the chord. It will divide the chord into two equal parts, d units each

d² + 16² = r²

d² = 20² - 16²

d² = 144

d = 12

Chord = 2d = 24 units

Measure of central angle and the corresponding chord related to the measure of the arc intercepted by the chord are the same, they're equal

Answer 2

The entire chord length is 12*2 = 24

The degree measure of a minor arc is equal to the measure of the central angle that intercepts it.

Explanation:

We can make a right triangle to solve for 1/2 of the chord length. The hypotenuse is 20 and one of the legs is 16

a^2+b^2 = c^2

16^2 + b^2 = 20^2

256 +b^2 = 400

Subtract 256 from each side

b^2 = 400-256

b^2 =144

Take the square root of each side

b = 12

That means 1/2 of the chord length is 12

The entire chord length is 12*2 = 24