Multiple choice

An equilateral triangle ABC, whose side is 6 cm is inscribed in a circle. Find the radius of the circle.

  1. $2$
  2. $2\sqrt3$
  3. $3$
  4. $3\sqrt2$
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B Correct answer
Explanation

For an equilateral triangle with side a, the circumradius R = a / sqrt(3). Here R = 6 / sqrt(3) = 2*sqrt(3).

AI explanation

The formula for the radius of a circle in which an equilateral triangle of side s is inscribed is R equals s divided by the square root of 3. Substituting the given side length of 6 cm into the formula gives 6 divided by the square root of 3. Rationalizing the denominator by multiplying the numerator and denominator by the square root of 3 gives 2 times the square root of 3 cm. The result is 2 times the square root of 3.

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