Question

Determine the radius of a circle if a chord is 24in and is 9in away from the center?

Answer 1

Given:

length of chord = 24 in

distance of the chord from the center = 9 in

Let the radius of the circle be r

Let us begin by illustrating the information in a diagram:

From the diagram, we can extract the right-angled triangle with the dimensions as shown:

To find r, we have to apply Pythagoras theorem.

The Pythagoras theorem states that:

`hypothenuse^2\text{ = opposite}^2\text{ + adjacent}^2`

Where hypothenuse is side with the longest length

Applying the pythagoras theorem:

`\begin{gathered} r^2\text{ = 12}^2\text{ +9}^2 \\ r^2\text{ = 225} \\ r\text{ = }√(225) \\ r\text{ = 15} \end{gathered}`

Hence, the radius of the circle is 15 in