### An equilateral triangle is inscribed in a circle of radius 18 cm. Find the length of the triangle's side.

**Answer:**

18√3 cm

**Step by Step Explanation:**

- ΔABC is inscribed in a circle. Lets O is the center of the circle.
- Now, connect all vertices of the triangle to O, and draw a perpendicular from O to 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.

= cos30° =BD OB √3 2

BD = OB ×√3 2

= 18 ×√3 2

= 9√3 - Therefore, BC = 2BD = 2(9√3) = 18√3 cm