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**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**

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

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