I would have thought that, if the problem can be drawn on a sheet of paper then the calculator I found would be OK for all practical purposes. I don't think that extreme cases apply here. The chord length is the distance between the centres of the smaller circles. the height of the chord is the distance from the large circle minus the smaller circle radius. So we are calculating the radius of a circle concentric to the large one, where the periphery passes through the centres of the small circle. the large circle is this calculated radius plus the radius of the small circle.

I presume the OP knows all the dimensions and can substitute them in the calculation app.

The problem may be a fascinating exercise, but the practicalities of mathematics faded for me when it got to imaginary numbers. I was alright with algebra, geometry and calculus, but that was 60 years ago and I haven't had the need to do much more than arithmetic, sines, cosines and tangents and a bit of Pythagorean juggling in the intervening time.

This was my today project, from circuit diagram to pcb. It is a logic indicator circuit (Hi-Lo_Pulse) using a 4011.
Click image for larger version. 

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Cheers,

Rob-T