To address the first image you shared, the expression provided is:

$\frac{5\sqrt{2}-5}{2} \quad \text{or} \quad \frac{\sqrt{2}-1}{2} = 1.025 \quad \text{which simplifies to} \quad 1.1 \, \text{cm}.$

This shows the calculations leading to an approximate result of 1.1 cm.

For the second image, which asks for the radius of the largest circle that fits in the middle of a square with side length of 10 cm:

This arrangement suggests the largest circle is tangent to all four sides of the square, and the diameter of the circle will be equal to the side length of the square. Since the side length is 10 cm, the diameter of the circle is also 10 cm. Therefore, the radius of the circle is half of the diameter:

$\text{Radius of the circle} = \frac{10}{2} = 5 \, \text{cm}.$

So, the radius of the largest circle that can fit in the middle of the square is 5 cm.

Would you like further clarification or details on either of these problems?

Here are a few related questions:

1. How do you determine the diameter of a circle from its radius?
2. How would you adjust the calculations if the square's side length changed?
3. How can you calculate the radius for circles fitting in other geometric shapes?
4. How does the arrangement of circles affect the largest possible circle that can fit inside?
5. Could the expression in the first image be solved using a different method?

Tip: When solving for the radius of a circle inscribed in a square, remember that the diameter is equal to the side length of the square.