20. Given a regular pentagon; $M$ is an arbitrary point inside it (or on its boundary). Number the distances from point $M$ to the sides of the pentagon (or their extensions) in ascending order: $r_{1} \leqslant r_{2} \leqslant r_{3} \leqslant r_{4} \leqslant r_{5}$. Find all positions of point $M$ for which the value of $r_{3}$ is the smallest, and all positions of point $M$ for which the value of $r_{3}$ is the largest.
20. Answer: $r_{3}$ is the largest for the vertices of the pentagon, and the smallest - for the midpoints of the sides. By dividing the regular pentagon $A B C D E$ with its axes of symmetry into 10 triangles, it is sufficient to investigate points $M$ inside and on the boundary of one of them, for example, $A O K$ (Fig. 29). To compare the distances from a point $M$ inside a certain angle to its sides, it is enough to determine on which side of the angle bisector the point $M$ lies. Using this, we can confirm that the distances from the point $M$ to the sides of the pentagon $A B, A E, B C$, $D E, C D$ always increase in the following order:

$$
r_{1} \leqslant r_{2} \leqslant r_{3} \leqslant r_{4} \leqslant r_{6}
$$

The third largest distance $r_{3}$ will be the greatest when $M$ coincides with $A$, and the smallest when $M$ coincides with $K$.