Subject:	Re: Do you recognize ... (Thebault's problem of 1938)
Author:	Frans Gremmen
Date:	27 May 99 09:23:27 -0400 (EDT)

Antreas P. Hatzipolakis cites:

> The problem, published in 1938, remained
> unsolved for well over forty years until K. B. Taylor submitted a
> solution in 1983 K. B. Taylor, `Three circles with collinear
> centres',....

Some articles started with Dr. H. Streefkerk's solution of the Thebault problem in 1973. It can be found in issues of july 1973, november 1973, january 1974 and march 1974 of the Dutch magazine "Nieuw Tijdschrift voor Wiskunde".

The articles are all in Dutch. A very nice is the short one of Prof. dr. G. R. Veldkamp, it's a real beauty. It is a complete solution of Thebault's problem with some more in the issue of november 1973 p. 86-89.

Veldkamp starts from an extension of Ptolemy's theorem as follows: Instead of 4 points on a circle OMEGA, take 3 points together with a circle GAMMA tangent to OMEGA. Replace 3 of the 6 distances involved in Ptolemy's theorem by the length of the tangent from 3 points to GAMMA.

Best Regards,

Frans Gremmen, University of Nijmegen, The Netherlands.