Question

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

Answer 1

Given: The side length of the equilateral triangle a = 6 cm

Step 1: Apply the formula for the circumradius

Substitute the given value of a into the formula:

`R = 6/sqrt(3)`

Step 2: Simplify

To simplify `6/sqrt(3)`, multiply both the numerator and the denominator by `sqrt(3)`:

`R = (6 xx sqrt(3))/(sqrt(3) xx sqrt(3))`

= `(6sqrt(3))/3`

`R = 2sqrt(3)` cm

The radius of the circle is `2sqrt(3)` cm, which is approximately 3.46 cm.