I know that any 3-connected simple planar graph with a designated outside face (outer face) has a primal-dual (double) circle packing (Brightwell-Scheinerman Theorem).

Q1- But I am not sure whether we can pin point the location of the vertices of that outside face and then compute the location of the inner circles? Do you now if such a thing is possible or not?

Q2- What if the outside face is a triangle, is it then possible to give three touching circles (possibly with different sizes) in the plane as the circles representing these three vertices and then ask an algorithm to find the location of the other inner vertices?