10.4. A chord is at a distance $h$ from the center of a circle. In each of the two segments of the circle subtended by this chord, a square is inscribed such that a pair of its adjacent vertices lies on the chord, and the other pair of adjacent vertices lies on the corresponding arc of the circle. Find the difference in the lengths of the sides of the squares.
10.4. Answer: $\frac{8}{5} h$. Solution. Let the side lengths of the larger and smaller squares be denoted by $2 x$ and $2 y$ respectively, and the radius of the circle by $R$. Then the distances from the center of the circle to the vertices of the inscribed squares, lying on the circle, give the expressions:

$$
(2 x-h)^{2}+x^{2}=R^{2},(2 y+h)^{2}+y^{2}=R^{2}
$$

From this, we obtain: $x-y=\frac{4}{5} h$. Then the difference in the lengths of the sides of the squares will be $\frac{8}{5} h$.