What is the area of the largest square that can be fit in a circle of radius 6 cm?

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.

Here the radius is 6 cm and the
diameter 12 cm. Now if a square has sides s, the diagonal has a length sqrt (s^2 + s^2)
= s*sqrt 2

So s* sqrt 2 = 12

s
= 12 / sqrt 2

The area of the square with side 12/ sqrt 2
is = 144 / 2 = 72.

Therefore the area of the
largest square that can fit in a circle of radius 6 is
72.