# 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...

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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.

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