In the given figure, AB is an equilateral triangle. Two circle of radius 6 cm and 18 cm are inscribed in the triangle. What is the side of an equilateral triangle (in cm)?

36\(\sqrt {3}\)

Big circle touches all the side of triangle, it means it is in-circle of equilateral triangle.

So, inradius of equilateral triangle = \(\frac{a}{2\sqrt {3}}\)

⇒ \(\frac{a}{2\sqrt {3}}\) = 18

⇒ a = \({36\sqrt {3}}\)