In the given figure, ABC is an equilateral triangle. Two circles of radius 4 cm and 12 cm are inscribed in the triangle. What is the side (in cm) of an equilateral triangle?

Answer: Option B

Now, In ΔAOF,
∠AFO = 90°
∠OAF = 30°

⇒ AF = $$4\sqrt{3}$$  cm
⇒ AO = 8 cm
and AE = AO + OD + DO' + O'E
= 8 + 4 + 12 + 12
= 36 cm
⇒ Median = 36 cm
In equilateral Δ,
$$\begin{array}{rl}& \text{Median}=\frac{\sqrt{3}}{2}\times \text{Side}\\ & \text{36}=\frac{\sqrt{3}}{2}\times \text{Side}\\ & \text{Side}=\frac{72}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=24\sqrt{3}\text{ cm}\end{array}$$