# Loc(K)i and trigonometry

Geometry Level pending

The equation of a circle that passes through $$(0,1)$$ and $$(2,3)$$ and has its centre on the equation of locus of point which is equidistant from $$(-1,1)$$ and $$(4,-2)$$ is $$x^2+y^2 + 2gx + 2fy + c = 0$$.

If $$\tan^{-1} (2g) + \tan^{-1} (2f) + \tan^{-1}(c) = \tan^{-1}(A)$$, where $$A$$ can be written in the form of $$\dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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