Tom and Jerry both have equal top running speeds and are initially at points \(A\) and \(B,\) respectively, separated by a distance of \(d\).

They both spot each other and immediately start running at their top speeds. Jerry runs on a straight line perpendicular to the line \(AB\) and Tom runs in such a way that its velocity always points towards the current location of Jerry.

Let \(r(t)\) denote the distance between Tom and Jerry at time \(t\).

Find \(\displaystyle \lim_{t \to \infty} r(t)\).

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