Multiple choice

The side of a regular hexagon is $2$ cm. Then the ratio of the radius of circumscribed circle to the radius of inscribed circle is?

  1. $\displaystyle \frac{\sqrt{3}}{2}$
  2. $\displaystyle \frac{1}{2}$
  3. $2$
  4. $\displaystyle \frac{2}{\sqrt{3}}$
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D Correct answer
Explanation

For a regular hexagon of side s, circumradius R = s = 2. Inradius r = s * sqrt(3)/2 = 2 * sqrt(3)/2 = sqrt(3). Ratio R/r = 2 / sqrt(3).

AI explanation

For a regular hexagon, the radius of the circumscribed circle is equal to the side length, so it is 2 cm. The radius of the inscribed circle, also known as the apothem, is given by the formula side multiplied by the square root of 3 divided by 2, which yields a value of the square root of 3 cm. The required ratio is the circumscribed radius divided by the inscribed radius, resulting in 2 divided by the square root of 3.

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