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Three circles are placed on a plane in such a way that each circle just touches the other two each having a radius of 10 cm. Area of the region enclosed by them.

  • Maths -

    the circle centers form an equilateral triangle with side 10.
    area of triangle is thus √3/4 10^2 = 25√3

    each side of the triangle subtends an angle of π/3, and the segment formed has area 1/2 *25*(π/3-√3/2) = 25/12 (2π-3√3).

    Subtract the area of the 3 segments from the triangle, leaving

    25√3 - 25/4 (2π-3√3) =~ 36.5

    you can massage that if you want.

  • Maths -

    oops - I used a diameter of 10 cm. Adjust accordingly.

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