Multiple choice

If a square ABCD is inscribed in a circle and AB = 4 cms, the radius of the circle is :

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

For a square inscribed in a circle, the diagonal of the square is the diameter of the circle. Diagonal = side * sqrt(2) = 4 * sqrt(2). Radius = diameter / 2 = 2 * sqrt(2).

AI explanation

When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Using the Pythagorean theorem for the right triangle formed by two sides of the square, the diagonal is sqrt(4^2 + 4^2) = sqrt(32) = 4 * sqrt(2) cm. The radius is half of the diameter, so r = (4 * sqrt(2)) / 2 = 2 * sqrt(2) cm.

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