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

6 cm

Step by Step Explanation:
1. ΔABC is inscribed in a circle. Let O be the center of the circle.
2. 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.
3. 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°
4. Since, triangle ODB is a right- angled triangle.
We have,

 BD OB
= cos 30° =
 √3 2

OB =
BD

 √3 2

=
3√3

 √3 2

= 6 cm
5. Therefore, the radius of the circle is 6 cm.