# Any way you slice it

Geometry Level 5

Suppose that two distinct lines passing through the origin cut through the region $$R$$ in the first quadrant bounded by the $$x$$-axis and the circle $$(x - 1)^{2} + y^{2} = 1$$ such that the lines divide $$R$$ into $$3$$ subregions of equal area.

If the sum of the slopes of these two lines is $$S$$, find $$\lceil 1000*S \rceil$$.

Note: Numerical methods can be used in the process of solving this question.

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