Question 287595
The diagonal of the square is the radius of the circle. The diagonal of the square is also the hypotenuse of an isosceles triangle. Let x be the length of the sides. Then by the Pythagorean Theorem we have:

x^2 + x^2 = 10^2 

2*x^2 = 100
x^2 = 50

But x^2 is also the area of the square.