There are infinite circles with center R and with any radius.
Given two circles are 5 and 6.
The blue circles numbered 1 to 4 are all possible solutions. These are infinite in number. They are within circle 5 or circle 6. Also they are outside circle 5 and outside circle 6.
The centers of all circles ie., P, Q and R are collinear.
obviously the common tangent is perpendicular to the line joining all centers of all circles.
Also you find two more circles numbered 7 and 8., These are tangentially touching circles 5 and 6, as well as the common tangent of circles 5 and 6.