those sections should be part of sphere that roles along those three surfaces.
So each section is an arc.
the shortest distance of the arc’s center to the 3 surfaces is start, tangent, end on the 3 surfaces.
or in other, rhino words:
if you pull the center (violet) of the arc back to the 3 surfaces you should get start, endpoint of arc, and intersection of arc and surface. (blue)
if the pulled center does not hit the arc (cyan/green points) the section is wrong.
fare from a robust algorithm … some a simple result full-filling above rule
I see a huge potential in some nice new (nurbs) surface Functions.
(@pascal - my chrismas-wish 
as patch did not make it)
TritangentSurface
Sphere tangent to 4 Surfaces
Fillet with given first rail ( @jordi.rovira “something similar, but with an additional thing”)