# Lines Tangent to a Circle

There are two lines of slope $- \frac{2}{5}$ that are tangent to a circle of radius $1$ centered at the origin $(0,0)$. Only one of these lines has a positive $y$-intercept. Let the point of tangency of this line to the circle be $(x,y)$. When $x+y$ is written in the form $\frac{a \sqrt{b}}{c},$ where $\gcd(a,c)=1$ and $b$ is not divisible by the square of any prime, what is $a+b+c?$

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