what size square fits in a circle

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Best answer


The maximum square that fits into a circle is thesquare whose diagonal is also the circle’s diameter. The length of a square’s diagonal, thanks to Pythagoras, is the side’s length multiplied by the square root of two. Set this equal to the circle’s diameter and you have the mathematical relationship you need.

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  • What is the maximum square that fits into a circle?

  • The maximum square that fits into a circle is the square whose diagonal is also the circle’s diameter. The length of a square’s diagonal, thanks to Pythagoras, is the side’s length multiplied by the square root of two.

  • What is the radius of the square inside the circle?

  • Hence the diagonal of the square is found to be equal to 18.38 cm. Now as said earlier, the diameter of a circle is always equal to the diagonal of the square drawn inside it. So the diameter of the circle is equal to 18.38 and now we can find the radius r of the circle by dividing its diameter by 2 as shown below:

  • What is the area of a circle with a side length?

  • Hence the area of the circle, with a square of side length equal to 13cm, is found to be 265.20 sq.cm. You can try the same kind of problems with the different side lengths of square drawn inside the circle.

  • When a square is circumscribed by a circle?

  • Do It Faster, Learn It Better. When a square is circumscribed by a circle , the diagonal of the square is equal to the diameter of the circle. Find the side length s of the square.

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