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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