The lamb and the wolf

A wolf is chasing a lamb in a field.
Say the field is a circle, the wolf and the lamb chose their initial location freely but ignoring the other. Then the chasing starts ...
The wolf and the lamb, each in his turn, moves at most 1 meter in any wanted direction. Does the wolf eat the lamb in a finite time ?

A simple method, the wolf directly aiming to the lamb seems to reach an infinite chasing with the distance from wolf to lamb decreasing forever, without ever becoming null.
The two chums finish to turn one after the other around the field without the wolf being able to catch the lamb.

Is there some better strategy for the wolf ?
What is the best strategy for the lamb to live long enough, so the shepherd comes to rescue ?





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