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Math Geometry

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Four circles of unit radius are drawn with centers (1,0), (-1,0), (0,1), and (0,-1). A circle with radius 2 is drawn with the origin as its center. What is the area of all points which are contained in an odd number of these 5 circles? (Express your answer in the form "a pi + b" or "a pi - b", where a and b are integers.)

I want a clear explanation with the answer. Thanks!

  • Math Geometry -

    Each small circle has area pi

    The intersections each have area pi/2 - 1, so the 4 areas of intersection have area 2pi-4

    The large circle has area 4pi.

    The points outside all the small circles lie only in the big circle.

    the points in each of the intersections lie in 2 small circles and the big circle.

    So, now you know which areas to add up.

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