Four points A, B, C and D lie on a straight line in the X-Y plane, such that AB = BC = CD, and the length of AB is 1 metre. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points B and C. The ant would not go within one metre of any insect repellent. The minimum distance in metres the ant must traverse to reach the sugar particle is

Dear student, 

Let us draw the figure to represent this question. 


Ant travels from A to P in such that, at any time, distance of the ant from B is 1m.

This means, AP is part of a circle with centre at B, since it maintains a fixed distance from a given point. So, AP forms quarter of a circle, and the circumference $=\frac{2\pi r}{4}=\frac{\pi }{2} (Since, radius(r) = 1)$

Similarly, QD is also $\frac{\pi }{2}$. When it reaches P, it is already 1m away from B. So, it can travel in a straight line to Q, and the distance PQ is 1m.

So, total distance the ant has to cover is $\pi + 1$.
Regards