Multiple choice

The area of a circle whose radius is $6 $ cm is trisected by two concentric circles. The radius of the smallest circle is

  1. $\displaystyle 2\sqrt{3}$ cm
  2. $\displaystyle 2\sqrt{6}$ cm
  3. $2$ cm
  4. $3$ cm
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A Correct answer
Explanation

The area of the circle is pi * 6^2 = 36pi. Trisection means each region has area 12pi. The smallest circle has area 12pi, so pi * r^2 = 12pi, r^2 = 12, r = sqrt(12) = 2 * sqrt(3).

AI explanation

The total area of the largest circle is pi * 6^2 = 36 * pi. Trisecting the area means the smallest circle has an area of 12 * pi. Setting pi * r^2 = 12 * pi gives r^2 = 12, so the radius is 2 * sqrt(3) cm.

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