Multiple choice

A circle is inscribed in an equilateral $\triangle ABC$. If the side of the triangle is 21 cm, what is the radius of the circle?

  1. $\dfrac{21}{2 \sqrt 3} cm$
  2. $\dfrac{21}{3 \sqrt 2} cm$
  3. $\dfrac{21}{2 \times 3} cm$
  4. $\dfrac{21}{\sqrt 2 \times \sqrt 3} cm$
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A Correct answer
Explanation

For an equilateral triangle, the inradius r = side / (2 * sqrt(3)). With side = 21, r = 21 / (2 * sqrt(3)).

AI explanation

The radius of an inscribed circle in an equilateral triangle is given by the formula side divided by two times the square root of three. For a side length of 21 cm, the radius is 21 divided by two times the square root of three cm.

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