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Re: A Problem
Posted:
May 3, 1999 12:57 AM


xpolakis@hol.gr (Antreas P. Hatzipolakis) wrote:  Bill Dubuque wrote:  >xpolakis@hol.gr (Antreas P. Hatzipolakis) wrote:  >  > In a triangle ABC, let D be a point on BC lying between B and C.  > If K_1,K_2 are the centers of the circles situated on the same side of  > BC as A and tangent to BC, to AD and internally to the circumcircle of  > ABC, prove that K_1 K_2 goes through the incenter of ABC.  > (V. Thebault, 1938)  >  > This is the famous "Thebault Problem" [...]   Now that you Bill revealed the Problem's difficulty nobody will try... :)  Who knows... had someone tried probably would be able to give a simple  solution..... [...]
I don't follow your logic. There are plenty of amateurs who (still) attempt elementary proofs of FLT. None of them seem discouraged by its reputation of extreme difficulty (which, like beauty, is in the eye of the beholder). In fact it should provide further inspiration to wouldbe solvers to know that, although the Thebault Monthly problem was unsolved for 45 years and although the first proposed solution spanned 24 pages, short elementary proofs *are* now known. Given this knowledge, unlike searching for an elementary proof of FLT, one has the satisfaction of knowing one is not on a wild goose chase. Go (re)discover this beauty if you like.
Since the entirety of your original post consisted merely of a statement of the problem, it wasn't clear whether or not you had any knowledge of work on the problem. Hence I replied with some general background info. What did you expect? Surely the same scenario would occur if someone posted just the statement of any other famous problem. Without explicitly specifying the intent of your post you leave its interpretation open to the reader. Caveat poster.
Bill Dubuque



