Question

A chord 20 inches long is 4 inches from the center

of a circle, as shown below. What is the radius of
the circle, to the nearest tenth of an inch?

Answer 1

The radius of the circle is 10.8 inches

Explanation:

Given:

Length of the chord = 20 inches

Distance of the chord from the center of the circle = 4 inches

To find:

radius of the circle=?

Solution:

As shown in the figure below, the radius, r, is the hypotenuse of a right triangle. One leg of the triangle is 4 and the other is half o f20 , or 10. Using the Pythagorean theorem to calculate the length of R, as follows:

`(4)^2 +(10)^2= (R)^2`

`16 +100= (R)^2`

`116= (R)^2`

`R =√(116)`

R= 10.77

R = 10.8 inches