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:
[tex]hypothenuse^2\text{ = opposite}^2\text{ + adjacent}^2[/tex]
Where hypothenuse is side with the longest length
Applying the pythagoras theorem:
[tex]\begin{gathered} r^2\text{ = 12}^2\text{ +9}^2 \\ r^2\text{ = 225} \\ r\text{ = }\sqrt{225} \\ r\text{ = 15} \end{gathered}[/tex]
Hence, the radius of the circle is 15 in
