$A B$ and $C D$ are two parallel chords located on opposite sides of the center $O$ of a circle with radius 15. $A B = 18, C D = 24$.

Find the distance between the chords.
Through the center $O$ of the circle, we draw a diameter perpendicular to the given chords. It intersects the chords $A B$ and $C D$ at their midpoints $M$ and $N$. Note that

$15^{2}=12^{2}+9^{2}$. Therefore, the right triangles $O M B$ and $O N D$ have legs of 12 and 9, and the desired distance $M N=O M+O N=12+9=21$.

![](https://cdn.mathpix.com/cropped/2024_05_06_4fce0705b02fa9e106d4g-08.jpg?height=640&width=646&top_left_y=1967&top_left_x=709)

## Answer

21. 

Problem