Question

A 30-inch chord in a circle is 8 inches from the center of the circle, as shown in the following figure.

Vhat is the length, in inches, of the radius of the circle

Answer 1

17 inches

Explanation:

See the attached image. Connect the center of the circle to one endpoint of the chord. That forms a right triangle because the radius is drawn perpendicular to the chord -- that's how the distance from center to chord is measured.

The radius splits the chord into two equal parts, each 15 inches long.

The right triangle has legs 8 and 15, so use the Pythagorean Theorem.

`r^2=8^2+15^2\\r^2=64+225\\r^2=289\\r=√(289)\\r=17`