I'm looking to check a diameter larger than the sum of the two largest gage pins in my set. So, I'd like to use three. I can't find the formula to do it.

The tables on the topic in the machinist handbook only deal with diameters of equal size. Can someone point me to the formula to calculate the smallest diameter which will be tangent to three inscribed (unequal) diameters (see drawing)

To be honest, I would figure it out using AutoCAD TTR function. I usually use it for double ball method on internal tapers.

I would too, if I had it.