The circle equation is $\"\"$ .

Rewrite the equation as $\"\"$ .

Compare it with circle equation $\"\"$ .

$\"\"$ .

Diameter of circle $\"\"$ .

Let the side of square be $\"\"$ .

In this case the squares diagonal is diameter of the circle.

The diagonals of a square bisects each other and the diagonals split the square into two right angle triangles.

Diameter of circle is hypotenuse of the triangles.

From the Pythagorean theorem $\"\"$ . $\"\"$

$\"\"$

$\"\"$ .

Area of the square $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ .

$\"\"$

Area of the square is $\"\"$ square units.