2. (17 points) Point $M$ lies inside segment $A B$, the length of which is 40 cm. Points are chosen: $N$ at the midpoint of $A M, P$ at the midpoint of $M B, C$ at the midpoint of $N M, D$ at the midpoint of $M P$. Find the length of segment $C D$ in cm.
Answer: 10.

## Solution.

![](https://cdn.mathpix.com/cropped/2024_05_06_db1c2ded2a2ccff3a78cg-1.jpg?height=48&width=588&top_left_y=2055&top_left_x=503)

$$
\begin{aligned}
& N P=N M+M P=\frac{1}{2} A M+\frac{1}{2} M B=\frac{1}{2} A B=20, \\
& C D=C M+M D=\frac{1}{2} N M+\frac{1}{2} M P=\frac{1}{2} N P=10 .
\end{aligned}
$$