Three boys are standing on a circular boundary of a fountain. They are at equal distance from each other. If the radius of the boundary is 5 m, the shortest distance between any two boys is :

A. $$\frac{{5\sqrt 3 }}{2}m$$

B. $$5\sqrt 3 \,m$$

C. $$\frac{{15\sqrt 3 }}{2}m$$

D. $$\frac{{10\pi }}{3}m$$

Answer: Option B

Solution(By Examveda Team)

Let A, B and C denote the portions of the three boys
Then, AB = BC = AC
So, ΔABC is equilateral
Let the side of ΔABC be a
Then,
$$\eqalign{ & \frac{a}{{\sqrt 3 }} = 5 \cr & \Rightarrow a = 5\sqrt 3 \cr} $$
∴ Required shortest distance = $$5\sqrt 3 \,m$$