# Suppose a chord of a circle is 5 inches from the center and is 24 inches long. How do you find the length of the radius?

Jun 19, 2016

#### Explanation:

There is a theorem which states that the line drawn from the centre of a circle, perpendicular to a chord, bisects the chord.

The distance of 5 inches must be the perpendicular distance, which means that the chord is bisected. 24 ÷ 2 = 12

An isosceles triangle is formed using 2 radii and the length of the chord as the base of the triangle, 24 inches, with the altitude. or height of the triangle being 5 inches.

This gives two right-angled triangles, with sides 5 inches and 12 inches and with the radius as the hypotenuse.

Using Pythagoras' Theorem:

${h}^{2} = {12}^{2} + {5}^{2} = 169$

$h = \sqrt{169} = 13$