Finding common areas.

Calculus Level 3

Two congruent circles \(C_1\) and \(C_2\) of radius \(R\) intersect at two points such that the center of either circle passes through the center of the other one. If the area of the region common to both circles can be represented as

\[ \text{Area} = R^A \left( \dfrac{B \pi - C \sqrt{C} }{D} \right) \]

where \(A, B, C\) and \(D\) are positive integers and \(C\) is square free.

Express your answer as \(A+B+C+D\).

Details:

  • You may need to carry out the necessary subtraction in order to make one common denominator. There is no such restriction to any pairs of integers being co-prime to one another.
  • The diagram shown above is just for illustration purposes only.
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