Classic Geometry

Geometry Level 3

There are two circles of radius one, which intersect at two points, with the centre of one lying on the circumference of the other. The area of the wedge shaped region common to both the circles can be expressed in the form \(\Large\frac{a\pi-b\sqrt{b}}{6}\), where a and b are co-prime, non-negative integers, and b is not divisible by the square of a natural number.

Find the value of \(\large a^{b}+b^{a}\).

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