# Five Tangent Circles

A circle of radius 1 is drawn in the plane. Four non-overlapping circles each of radius 1, are drawn (externally) tangential to the original circle. An angle $$\gamma$$ is chosen uniformly at random in the interval $$[0,2\pi)$$. The probability that a half ray drawn from the centre of the original circle at an angle of $$\gamma$$ intersects one of the other four circles can be expressed as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a + b$$?

Details and assumptions

The half ray from the centre of the fifth circle at angle $$\gamma$$ goes only in one direction, not both.

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