Multiple choice

A circular area having a radius 20 cm is divided into two equal parts by a concentric circle of radius 'r'. The value of 'r' will be

  1. 5 cm

  2. 10 cm
  3. 5$\sqrt{2}$cm
  4. 10$\sqrt{2}$cm
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D Correct answer
Explanation

Area of the large circle = pi * 20^2 = 400pi. The inner circle divides it into two equal parts, so its area is 200pi. pi * r^2 = 200pi, so r^2 = 200, r = sqrt(200) = 10 * sqrt(2).

AI explanation

The area of the larger circle is pi * 20^2 = 400 * pi. The concentric circle divides this area in half, so its area must be 200 * pi. Setting pi * r^2 equal to 200 * pi gives r^2 = 200, so r is 10 * sqrt(2) cm.

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