Prove that the sum of the perimeters of the smaller circles in the Bigger circle is equal to that of the bigger circle. (The centres are on the line given which is the diameter of the bigger circle.)

Given: perimeter of a circle = Dï

Given: d₁ + d₂ + d₃ + d₄ = D (the sum of the diameters of the smaller circles is equal to the diameter of the larger circle)

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The sum of the perimeters of the smaller circles would be:

   = d₁ï + d₂ï + d₃ï + d₄ï

            Applying the distributive method, gives...

   = (d₁ + d₂ + d₃ + d₄)ï

            With substitution, d₁ + d₂ + d₃ + d₄ = D, gives

   =  Dï

            Which is the perimeter of the larger circle. Thus the sum of the perimeters of the smaller circles equals the perimeter of the larger circle.

Posted by Dej Mar on 2006-02-14 01:36:56