Here's the first of four messages from Peter Moses. R. ---------- Forwarded message ---------- Date: Fri, 9 Sep 2011 12:34:44 +0100 From: "Moses, Peter J. C." <mows@mopar.freeserve.co.uk> To: Richard Guy <rkg@cpsc.ucalgary.ca> Subject: Re: Incircles problem Hi Richard,  

Panic over!  Well, not quite.   For the medians, the statement is indeed false, as Stanley's picture shows. However, for cevians of the incenter the statement is true.  The center of this ellipse is not in Clark's ETC.   Surprisingly, it is true for the Fermat point.(X(13), though not X(14)) and also for both the Soddy centers! Although certainly for Fermat and the outer Soddy center it is a conic rather than specifically an ellipse.   Best regards, Peter.     ----- Original Message ----- From: "Richard Guy" <rkg@cpsc.ucalgary.ca> To: "math-fun" <math-fun@mailman.xmission.com> Cc: "Julian Salazar" <julian.salazar@shaw.ca> Sent: Thursday, September 08, 2011 9:43 PM

Dear all,           Panic over!  Stanley Rabinowitz has used Geometer's sketch pad (see attached) to show that the statement is not true!  Sorry to have bothered you with it.     R.