Process for solving this system of equations I have this system of equations for which I'd like to solve for $x$,$y$, and $r$ where $a$,$b$, and $t$ are constants:
1: $0 = (x-a)^2 + (y - b)^2 - t^2$
2: $y = \dfrac{bx-rx+ar}{a}$
3: $r = \dfrac{x^2 + y^2}{2y}$
Could anyone help me get a point where one of $x$,$y$, or $r$ are defined in terms of $a$,$b$, and $t$?
I know this system is solvable in the reals (for some values of $a$,$b$, and $t$) , for example: a = 80 b = 100 t = 60, but I am unsure how WA is doing the steps of manipulation to solve.
Essentially the problem is given a circle centered at $(a,b)$ with radius $t$, find a circle which is tangent to the x-axis at $(0,0)$ and the other circle at some point $(x,y)$. 
Equation 1 is simply the equation of the original circle.
Since it is tangent to the x-axis it must be of the form $x^2 + y^2 - 2ry = 0$ where $r$ is the radius, which is where the above equation 3 comes from.
To obey tangency between the two circles, the slope from $(0,r)$ to $(a,b)$ must be the same slope as from $(0,r)$ to $(x,y)$ which is the source of equation 2.
Any insight or recommendations are greatly appreciated.
Edit: Oversight from before, tangent at (0,0)

$(3)\iff (\;(y\ne 0)\land (r^2=x^2+ (y-r)^2)\;).$ Subtracting this from (1) yields a linear equation in $x, y$ (with the extra condition $y\ne 0$),which, with (2), is a system  of 2 linear equations in 2 variables.
