Question

Suppose a chord is 20 inches long and is 24 inches from the center of the circle. How do you find the length of the radius?

Answer 1

`r = 26"`

Explanation:

A line segment from the 20" chord to the center of the circle is a perpendicular bisector of the chord creating a right triangle with legs of 10" and 24" with radius of the circle forming the hypotenuse.

We can use the Pythagorean theorem to solve for the radius.

`a^2 + b^2 = c^2`

a = 10"
b = 24"
c = ?"

`10^2 + 24^2 = r^2`
`100 + 576 = r^2`
`676 = r^2`
`sqrt676 = r`
`26" = r`