Problem 2.1. Points $A, B, C, D$ are marked on a line, in that exact order. Point $M$ is the midpoint of segment $A C$, and point $N$ is the midpoint of segment $B D$. Find the length of segment $M N$, given that $A D=68$ and $B C=20$.

![](https://cdn.mathpix.com/cropped/2024_05_06_acec579961a94b9a26d0g-06.jpg?height=210&width=832&top_left_y=323&top_left_x=315)

## 68
Answer: 24.

Solution. Let $AC = x$, then $AM = \frac{x}{2}$. Now we will calculate the length of $ND$:

$$
ND = \frac{BD}{2} = \frac{20 + CD}{2} = \frac{20 + (68 - x)}{2} = 44 - \frac{x}{2}
$$

Now it is not difficult to calculate $MN$:

$$
MN = AD - AM - ND = 68 - \frac{x}{2} - \left(44 - \frac{x}{2}\right) = 24
$$