In the diagram, $O$ is the centre of each circle. The circumferences of the circles are $24 \pi$ and $14 \pi$. $B$ is a point on the outer circle and $O B$ intersects the inner circle at $A$. The length of $A B$ is
(A) $\sqrt{10}$
(B) 5
(C) 7
(D) $10 \pi$
(E) 3

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-116.jpg?height=381&width=408&top_left_y=2344&top_left_x=1419)
The circumference of a circle is equal to $2 \pi r$, where $r$ is the radius of the circle.

Since the circumference of the outer circle is $24 \pi$, then its radius is 12 . Thus, $O B=12$.

Since the circumference of the inner circle is $14 \pi$, then its radius is 7 . Thus, $O A=7$.

Therefore, $A B=O B-O A=5$.

Answer: (B)