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You can choose any three points and draw a triangle. The closer these points the smaller triangle and its perimeter. So, perimeter can be almost 0. At the same time, perimeter cannot be essentially bigger than radius because such triangle cannot be inscribed. Let's say you build triangle with two sides almost 2r and third side - almost 0. This triangle will have perimeter ~ 4r or 4. Now we have range 4>P>0. Now you can see that P can be 0.001, 0.01 and 0.1

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