### An equilateral triangle with a side of length 6√3 cm is inscribed in a circle. Find the radius of the circle.

**Answer:**

6 cm

**Step by Step Explanation:**

- ΔABC is inscribed in a circle. Let O be the center of the circle.
- Now, connect all vertices of the triangle to O, and draw a perpendicular from O meet the side BC of the triangle at point D.
- We know, all the angles of an equilateral triangle measure 60°.

So, angle ACB = ABC = CBA = 60°

OB and OC are bisectors of ∠B and ∠C respectively,

∠OBD = 30° - Since, triangle ODB is a right- angled triangle.

We have,

= cos 30° =BD OB √3 2

OB =BD √3 2

=3√3 √3 2

= 6 cm - Therefore, the radius of the circle is
**6 cm**.