There are four dogs, each at a corner of a large square

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There are four dogs, each at a corner of a large square.

There are four dogs, each at a corner of a large square.

Each of the dogs begins chasing the dog clockwise from it.
All of the dogs run at the same speed. All continuously adjust their direction
so that they are always heading straight toward their clockwise neighbor.
How long does it take for the dogs to catch each other? Where does this happen?

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