I love to sometimes think of how I could construct simple Geometrical figures (a circle in the following case) under different 'circumstances' (or should i say constraints listed in a problem). The following two problems occured to me last night out of sheer thought.
Intuition (with a little imagination) tells me that the following two constructions are definitely possible (i.e. the give information is not insufficient AND there EXISTS a third circle as a solution to the two problems.)

I have two coplanar circles C1 and C2 having radii r1 and r2 with r2>r1 and distance between the two centres exceeding the sum of r1 and r2. I also have a point P in the same plane as that of C1 and C2 such that it lies in the exterior of both C1 and C2.
Draw a circle C3 that is tangential to C1 and C2 and passing through P.

The solution to the above problem might also extend to this problem:
I have two coplanar circles C1 and C2 having radii r1 and r2 with r2>r1 and C1 lying entirely inside C2 (thus they do not intersect at all). I have a point P that lies in the exterior of C1 but in the interior of C2.
Draw a circle C3 that is tangential to C1 and C2 and passing through P.

PS: I hope to have provided unambiguous and complete information in the above problems. :-) . Please post your reply to get clarified over any issues you might have.

Thanks,

Deep G.
d:-)

https://www.cut-the-knot.org/Curriculum/Geometry/Apollonius.shtml