1.13. Inside a circle with a radius of 15 cm, a point $M$ is taken at a distance of 13 cm from the center. A chord of length 18 cm is drawn through this point. Find the lengths of the segments into which point $M$ divides the chord.
1.13. Draw $O C \perp A B$ (Fig.

1.11). Then $C B=\frac{1}{2} A B=9 \quad \text{cm}$.

From $\triangle O B C$ it follows that

$O C=\sqrt{O B^{2}-B C^{2}}=12(\text{cm})$, and from

$\triangle O M C$ - that $M C=\sqrt{O M^{2}-O C^{2}}=5$ (cm). Therefore, $A M=9+5=14$ (cm), $M B=9-5=4$ (cm).

![](https://cdn.mathpix.com/cropped/2024_05_21_1e3d8d2f6605ac23e2a5g-420.jpg?height=452&width=452&top_left_y=109&top_left_x=689)

Fig. 1.11

Answer: 14 and 4 cm.