A circle has a diameter of 9cm

a square has a side of 5cm

use Pythagoras theorem to show that the square will fit inside the circle without touching the edge of the circle.

For the square to fit inside the circle without touching it, the diagonal of the square needs to be less than the diameter of the circle.

Using the Pythagorean theorem we can calculate the diagonal of the square:

X = SQRT (5^2 + 5^2)

X = SQRT (25 + 25)

X = SQRT (50)

X = 7.07

The diagonal of the square is 7.07 cm, which is less than the diameter of the circle, 9cm, so it will fit.