I think I have enough information to get an answer here, but the solution continues to elude me. I have a circle with radius r whose center is at (x,y). I also have two points outside the circle V0 (a, b) and V1 (a, c) that are a fixed distance away from the two points, K, and aligned vertically with one another. Note that I do not know the value of K, only that K is a fixed value.
Great. So, calculating the y component of the center is simple -
y = c - b
But I'm at a loss as to how to calculate the x component of the center! I can see how one could calculate angle a using some simple trig, but I'm not sure how I would use that to get to my goal which is to know the center of the circle. Can this be done without knowing K? It FEELS like this should be possible, but perhaps not.
Looking forward to seeing what people think!
Thanks, Marshall
I assume the $x$-coordinate of $V_0$ and $V_1$ is known. Denote it $x_V.$
The $x$-coordinate of the center is $x=x_V+h,$ where $h$ is the height of the isosceles triangle with sides $r,r,y_1-y_0.$