Given two non-intersecting circles of radii a and b (with centers A and B respectively) with c the distance between their centers.

1) Prove that there always exists two points (say P and Q) such that each can be used as a center of inversion that maps the non-intersecting circles into concentric circles.

2) Give the distance between P and Q in terms of a, b, and c.

2) The required distance between P and Q is √([a^2 - b^2 + c^2]^2 - 4a^2*c^2)/c]

Edited on January 9, 2023, 3:13 am

Posted by K Sengupta on 2023-01-09 03:10:32