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smc

geometry senior

Problem

A square has sides of length , and a circle centered at one of its vertices has radius . What is the area of the union of the regions enclosed by the square and the circle?
(A)
(B)
(C)
(D)
Solution
The area of the circle is ; the area of the square is . Exactly of the circle lies inside the square. Thus the total area is .
Final answer
B