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.

I don't understand how this fine geometry problem would elicit a rating of a mere D1.5.

Edited on January 9, 2023, 3:16 am

Posted by K Sengupta on 2023-01-09 03:16:05