Multiple choice

A square is inscribed in a circle of radius $2$ cm. Side of the square in cm is:

  1. $\sqrt{2}$
  2. $2$ $\sqrt{2}$
  3. $4$ $\sqrt{2}$
  4. $2$ $\sqrt{3}$
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B Correct answer
Explanation

When a square is inscribed in a circle, the diagonal of the square is the diameter of the circle. Diameter = 2 * radius = 2 * 2 = 4 cm. If side is s, then s * sqrt(2) = 4, so s = 4 / sqrt(2) = 2 * sqrt(2).

AI explanation

The diagonal of a square inscribed in a circle is equal to the diameter of the circle. With a circle radius of 2 cm, the diameter and thus the diagonal of the square is 4 cm. Using the Pythagorean theorem where the side length s squared plus s squared equals the diagonal squared, we get 2s squared equals 16. Solving for s gives a side length of 2 times the square root of 2 cm.

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