(V.Protasov, 8) For a given pair of circles, construct two concentric circles such that both are tangent to the given two. What is the number of solutions, depending on location of the circles?
/bump
Somebody help please. crastybow and I have some ideas but a lot are intuitive such as the radius of the smaller circle is on the perpindicular bisector of the line segment connecting the radii of the 2 given circles and a bunch more but before I go into too much I was kind of wondering if anybody else had a solution
If given circles have equal radii, then there are infinite number of solutions. Otherwise, the number of solutions is equal to the number of intersection points of the given circles. In the latter case, the common center of sought-for circles must be the reflection of an intersection point of the given circles across the midpoint of the segment joining their centers.