Unit Circle on Unit Square

Geometry Level 2

Select a random point from the interior of a unit square (uniformly across the area). Let \(p\) be the probability that a unit circle centered at that point will completely cover the square.

To three decimal places, what is \(p?\)

On the left, the unit circle completely covers the unit square.  On the right, the unit circle <em>does not</em> completely cover the unit square.

On the left, the unit circle completely covers the unit square. On the right, the unit circle does not completely cover the unit square.

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