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Perimeter Puzzle

There is a square and a circle. The two are scaled appropriately and translated so they touch at just three distinct locations.
They intersect at two adjacent corners on one edge of the square, and at the midpoint of the opposite edge.
The question is, what is the ratio of the circumference of the circle to the perimeter of the square?
What is the ratio of the perimeter of the circle to that of the square?