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Math. I really don't get this question

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three circles are manually tangent externally. their centers form a triangle whose sides are of length 8, 9, 13. find the total area of the three circles

  • Math. I really don't get this question -

    If the radii of the circles are x,y,z then each side of the triangle is the sum of two of the radii. So,

    x+y=8
    x+z=9
    y+z=13
    (x,y,z) = (2,6,7)

    Since the area of a circle is πr^2, the area of all of the circles is
    π(2^2+6^2+7^2) = 89π

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