A circle has diameter 11cm

A square has side length 7cm

Use Pythagoras' Theorem to show that the square will fit inside the circle without touching the edge of the circle.

c^2 = a^2 + b^2 c^2 = 7^2 + 7^2 = 49 + 49 c^2 = 98 c = sqrt 98 c = 9.8 cm c = diagonal of square (9.8 cm) and is less than the diameter of the circle (11 cm), so the square will fit inside the circle without touching the edge of the circle.

In this case, to prove what is required, we must use the Pythagorean theorem to find the diagonal of the square.

If the diagonal of the square is smaller than the diameter of the circle, then the square will fit perfectly in the circle without touching it.

Diagonal = Root ((7 ^ 2) + (7 ^ 2)) = 9.89 cm.

we observed that

9.89cm <11cm.

Therefore we show that:

the square will fit inside the circle without touching the edge of the circle