SOLUTION: Three circles of radius 2 cm overlap so that each passes through the centre of the other 2. The area of centre section is?

      Find the area of the common part of the three circles.

1.  Make a sketch. Let the points A, B and C are the centers of these circles.

    Connect the centers by straight line segments.

    You will get the equilateral triangle. 

    Why it is equilateral ?? - Because it has three sides of equal length.
                               The length of each side is equal to the radius, namely, 2 cm.


2.  Now, what is this common area of these three circles?

    It is THIS equilateral triangle PLUS three segments of the circles.

    On "segments of the circles" see the lesson

        Area of a segment of the circle 

    in this site.
    

3.  The area of each segment of the circle is equal to the area of the sector minus the area of the triangle.

    Our segments of the circles are special: they are 60 degrees.
    So, the area of each of the three segments is  of the area of the circle minus the area of the equilateral triangle with the side of 2 cm.


4.  Now I suppose, that after getting full, clear and comprehensive explanations you are able to complete the solution on your own.


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