380. Point $A$ was subjected to central symmetry with the center at point $O$, resulting in point $A^{\prime}$. Then point $A^{\prime}$ was subjected to central symmetry with the center at another point $O^{\prime}$, resulting in point $A^{\prime \prime}$. Find the distance between $A$ and $A^{\prime \prime}$, if the distance between $O$ and $O^{\prime}$ is $a$.
$\triangleright$ The distance between $O$ and $O^{\prime}$ is half the distance between $A$ and $A^{\prime}$, since $O O^{\prime}$ is the midline of triangle $A A^{\prime} A^{\prime \prime}$. Answer: $2 a . \triangleleft$

Sometimes central symmetry helps in solving construction problems (even if it is not mentioned in the problem statement):