97. a) It is clear that any plane broken line of length 1 can be enclosed in a circle of radius 1: for this, it is sufficient for the center $O$ of the circle to coincide with one of the ends of the broken line. What is the radius of the smallest circle in which any broken line of length $l$ can be enclosed?

b) It is clear that any plane closed broken line of perimeter 1 can be enclosed in a circle of radius $\leqslant \frac{1}{2}$: for this, it is sufficient for the center $O$ of the circle to coincide with any point of the broken line. (In this case, for any point $M$ of the broken line, the length of one of the two segments $O M$ of the broken line will be $\leqslant \frac{1}{2}$, and therefore the distance $O M$ will be $\leqslant \frac{1}{2}$.) What is the radius of the smallest circle inside which any closed broken line of length 1 can be enclosed?