A little patience, please: I'm incredibly old, it's a long time since I did basic algebra so I'm a little confused.

```
I have a line y = mx+c
and a circle (x-h)*(x-h)+(y-k)*(y-k) = r*r
I've expanded the circle: x*x-2*x*h+h*h+y*y-2*y*k+k*k = r*r
and substituted mx+c for y: x*x-2*x*h+h*h+(m*x+c)*(m*x+c)-2*(m*x+c)*k+k*k = r*r
expanding out: x*x-2*x*h+h*h+m*x*m*x+2*m*x*c+c*c-2*m*x*k+2*c*k+k*k = r*r
Now I want to get all x's on the one side so I can evaluate x:
x*x-2*x*h+m*x*m*x+2*m*x*c-2*m*x*k = r*r-h*h-c*c-2*c*k-k*k
I can refine it a wee bit further:
x*(x-2h+m*m*x+2*m*c-2*m*k) = r*r-h*h-c*c-2*c*k-k*k
```

But that's as far as I can go...