Multiple choice

Find the maximum area of a rectangle that can be inscribed in a circle of radius 10 cm

  1. $100$
  2. $200$
  3. $400$
  4. $1600$
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B Correct answer
Explanation

A rectangle inscribed in a circle has maximum area when it is a square. The diagonal of the square is the diameter of the circle, which is 20 cm. If side is s, s^2 + s^2 = 20^2, so 2s^2 = 400, s^2 = 200.

AI explanation

The rectangle of maximum area inscribed in a circle is a square, where the diagonal equals the diameter of the circle. With a circle radius of 10 cm, the diameter and thus the diagonal of the square is 20 cm. Using the Pythagorean theorem, the side of the square is 20/√2 cm, making the maximum area (20/√2)^2, which equals 200 sq cm.

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