Two squares of side 1 have a common centre. Show that the area of their intersection is greater than 3/4.
Notice that one of the squares can be obtained from another by rotating around their common centre.
This rotation maps the circle inscribed into the square to itself.
Therefore, the area of the intersection of the squares is greater than the area of the circle, which is, of course, equal to π/4, and which in turn is greater than 3/4.
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