How many square units are in the area of the largest square that can be inscribed in a circle with radius 1 unit?
I want to find the side length of the largest square that can fit inside a circle with radius 1. I know that the diagonal of the square will be equal to the diameter of the circle, which is 2 units. I can use the Pythagorean theorem to relate the side length of the square to its diagonal. If I let x be the side length of the square, then I have x^2 + x^2 = 2^2, or 2x^2 = 4. Dividing both sides by 2, I get x^2 = 2, or x = sqrt(2). The area of the square is x^2, which is 2 square units. 