From the previous post "Circle And Circle In A Closed Curve" dated 11 Jun 2026,
An infinitesimal change in length \(ab\) produce a similar infinitesimal change at intercepts \(a'\) and \(b'\) and such a change is reversible, change in length \(a'b'\) is continuous as length \(ab\) changes continuously. The change in length between the red and blue centers is smooth as the closed curve is smooth.
Can the two centers be made to meet by changing length \(ab\) or points \(a\) and \(b\)? Can you drive the red center into the blue center by manipulating point \(a\) and \(b\)?
Note: Only when \(ab=a'b'\) guarantees a square; when blue and red are the same circle.
