Question

Calculate the fit of the square in the circle?

Answer 1

If the diagonal of the square has a length less than the diameter of the circle, it will fit inside without touching

Diameter = 9

Diagonal² = 5² + 5² = 50

Diagonal = 5sqrt(2)

5sqrt(2) < 9

Because

[5sqrt(2)]² < 9²

50 < 81

Answer 2

To find the area of the largest square that can be fit in a circle, let's see what happens when the square is drawn. We find that for a square all four corners of which lie on the circle, the diagonal of the square is equal to the diameter of the circle. The area of the square with side 12/ sqrt 2 is = 144 / 2 = 72.

Explanation: