Final answer:
The size of the largest square that can fit within a circle has each side equal to the circle's diameter, which is twice the radius of the circle. The correct answer is b) Side length equals the circle's radius.
Step-by-step explanation:
The question at hand is: How big of a square can fit in a circle? To find the size of the largest square that fits entirely within a circle, we must relate the side length of the square to the circle's diameter, because that's the longest straight line that can be drawn inside the circle. The corners of the square will touch the circle exactly if the side length of the square is equal to the diameter of the circle. Since the diameter is twice the radius, option a) Side length equals the circle's diameter is correct. The side length of the square is equal to the diameter (2r) of the circle it is inscribed within.
A square with a side length equal to the circle's radius can fit perfectly inside a circle. The diameter of the circle is equal to twice the radius, so the square's diagonal will also be equal to twice the radius. This means that the square's diagonal will fit neatly across the circle's diameter, ensuring that the square can completely fit within the circle. A square with a side length equal to the circle's radius is the largest square that can fit inside a circle.