Question: Can this theorem by proved?

Problem Q15 in the book Parabolic Problems by David Angell and Thomas Britz describes a large circle (LC) and several smaller circles (SCs) which are each tangent to its neighbour SC(s), and externally to LC. All circles are tangent to the x axis and above it.

Section one of this worksheet displays the LC and six of the SCs based on the book's formula for the diameter of the latter in terms of the diameter of the LC and the largest SC, which is determined by the user.

Section two finds and displays that all of the displayed SCs' centers lie on the diameter of a circle closely related to the LC and larger than it.

Can this be proved to be the case for any sizes of the LC and SCs in the same formation as that displayed?

Parabola_Problems_Q15.mw

Please Wait...