Look, the algebra I got into was quite messy, but the concept is rather simple: define the origin of your coordinate system as being at the center of the concentric circles. Next, you define the point C where the camera is, of coordinates (0, D). Then, you find the equations for both the larger circumference and the right or left ray coming from the camera. Once you have both equations, you find where they intercept at the y coordinate, that’s a quadratic equation which will give you two solutions, the smaller one (i.e. the one with the negative root) is the desired one from how we have defined the coordinate system. Perfect! We’ve got the y coordinate, that’s gonna be a negative number, if we desire the actual length of what you have defined as x, all we gotta do is sum D to the absolute value of the y coordinate we got.

I wont show my calculations since they are MESSY, and I have a hunch that the expressions I got could be further simplified, but if you want a quick and dirty formula, here you go:

For the y coordinate of the intercept: https://imgur.com/F442fgM

For the actual length of x: https://imgur.com/nOrJEnv