# Limited Geometry

Geometry Level 3

Find the radius of a circle which passes through the point $$(2,0)$$ and whose centre is the limit of the point of intersection of the line:

$$3x+5y=1$$ and $$(2+c)x+5{c}^{2}y=1$$ as $$c\rightarrow 1$$.

The radius of the form $$\frac { a\sqrt { b } }{ d }$$ where $$a$$ and $$d$$ are positive co-prime integers and $$b$$ is not a perfect square.

Find: $$a+b+d$$.

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