As in the image, I have a circle that intersect the $y$ axis (or could be a vertical line). I know center and radius of that circle. There is a second smaller circle, inside the bigger one, tangent to the $y$ axis (or vertical line) and to the bigger circle. I know the coordinate $y_A$ where the smaller circle intersect the vertical line. I have to calculate the radius of the smaller circle $r$. I try to do it using trigonometry, but I found a solution to be iterate. I'm looking for a "direct" solution.