The sharp circle square
Let there be a square with a side length of 1. For each side, mark its midpoint and cast a ray outward perpendicular to the side. Mark a point on each ray with distance from its respective midpoint, and pass a circle through the points of the side and the point we just marked. Find an , so that the center of circle is on the midpoint of the opposite side of the square.
The answer is 0.125.
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