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Question:** A square with a side length of 10 cm is inscribed in a circle. Determine the area of the circle.

Solution:

When a square is inscribed in a circle the diameter of the circle is equal to the diagonal of the square. We first calculate the diagonal of the square.

For a square with side length \( s = 10 \) cm the diagonal \( d \) is given by:

\[

d = s\sqrt{2} = 10\sqrt{2} \ \text{cm}

\]

This diagonal is the diameter of the circle. The radius \( r \) of the circle is half of the diameter:

\[

r = \frac{d}{2} = \frac{10\sqrt{2}}{2} = 5\sqrt{2} \ \text{cm}