> the solution is only possible if the intersection is of equal distance from each point
It's the definition of the center of a circle :)

Your tangent tool circle is like a rolling ball bearing :)
I suppose that is its use :)
Many circles are possible in my funny example without 2 specifics points
(circle tangent between big curves restangle/circle)
Geometry is always amazing :)
Thx for te explanations & precisions