Lines Tangent to a Circle

Geometry Level 4

There are two lines of slope 25- \frac{2}{5} that are tangent to a circle of radius 11 centered at the origin (0,0)(0,0). Only one of these lines has a positive yy-intercept. Let the point of tangency of this line to the circle be (x,y)(x,y). When x+yx+y is written in the form abc,\frac{a \sqrt{b}}{c}, where gcd(a,c)=1\gcd(a,c)=1 and bb is not divisible by the square of any prime, what is a+b+c?a+b+c?

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