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Please help me work out this problem

The problem is like this

There is a square table. On each vertex there is an ant sitting. Now these ants (four of them) starts moving in such a way that at any instant of time the direction of motion of each ant is directed towards an ant which started from a vertex adjacent to it (say the vertex to its right side).

Now the question is:

to find the path traced out by each ant (all of them will trace similar paths).

I tried drawing the paths of each ant to solve this, from the drawings i can only understand that at any time the velocity vector of two adjacent ants are perpendicular to each other and the four of them will eventually meet at the center of the square.

regards

Mahesh

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# Find the path traced out by each ant

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