Task 2. Two segments $\overline{A B}$ and $\overline{C D}$ of equal lengths lie on the same line, such that $\frac{1}{4}$ of their lengths is shared. Determine the length of these segments if the distance between their midpoints is 6 cm.
Solution. Let $x$ be the length of the segment $\overline{C B}$. Then the length of the segment $\overline{M N}$, which is $6 \mathrm{~cm}$, expressed in terms of $x$ is $3 x$. From here we have that $3 x=6$, so $x=2 \mathrm{~cm}$. The length of the segment $\overline{A B}$ is twice the length of the segment $\overline{M B}$, or 4 times the length of the segment $\overline{C B}$. Therefore, the length of the segment $\overline{A B}=4 \cdot 2=8 \mathrm{~cm}$. Since from the condition of the problem the segments $\overline{A B}$ and $\overline{C D}$ are equal, it follows that the segment $\overline{C D}=8 \mathrm{~cm}$.

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