math help please

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#1254

From: Paul Bruckman
Date: Mon, 15 Jun 1998 00:00

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consider the Malfatti circles inscribed in a given triangle ABC. Let
A'B'C' be the triangle formed by their centers (corresponding to the
vertices A,B,C in the obvious way).  Suppose Angles A <=B<=C and A<C.
Prove that Angles C'-A' < C-A .

Can anybody see a quick solution? It seems to me that the conclusion is
that if the Malfatti circles of triangle A'B'C' are also drawn and the
process repeated indefinitely, the result (if true) would imply that
the limiting triangle would be a point (the incenter I of triangle ABC),
but also that the limiting triangle would approach an equilateral
triangle.   Sincerely, Paul Bruckman

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From: Paul Bruckman <aardwolf@gte.net>
Subject: math help please
Date: 1998/06/15
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