# Supporting the $$\sin$$

Geometry Level 5

Refer to the image above (not drawn to scale)

The $$2$$ circles above are tangent to the graph $$y=\sin(x)$$. The two circles share $$1$$ point of tangency $$(a, b)$$, and the ratio of the area of the smaller circle to the area of the bigger circle is $$\frac{1}{4}$$.

Given that there are two possible values for $$b$$, ($${b}_{1}$$ and $${b}_{2}$$), and that $${b}_{1}>{b}_{2}$$, and that the sum of the area of both the circles can be expressed as $$A$$, find $\left\lfloor 10000\left( A+ \left( {b}_{1} - {b}_{2}\right)\right) \right\rfloor$

$${\scriptsize\text{ Congratulate yourself after you solve this}}$$

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