I have tough question, which I need for a program I am working on.
I have one circle where I know its center position $(x,y)$ and radius, and one straight line with the formula $y=x+b$ where $b$ is known.
Now I need to find out the center position of another circle so that it touches both the line and the first circle. For this second circle I know only the radius.
Circle 1: Radius $r_1,C_1(x_1,y_1)$
Circle 2: Radius $r_2$
Line: $ly=lx+b$ ($b$ is a known lenght)
What I need to find is $C_2(x_2,y_2)$
At a later point I will also need to find the centerpoint of a circle touching $2$ known circles, but I hope the answer to the first part will help in this as well.