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Topic: A Theorem concerning the Trisectors of a Triangle
Replies: 24   Last Post: Nov 10, 1998 12:19 AM

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 Antreas P. Hatzipolakis Posts: 1,376 Registered: 12/3/04
Re: A Theorem concerning the Trisectors of a Triangle
Posted: Sep 18, 1998 9:09 PM

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Beitra"ge zur Algebra und Geometrie Contributions to Algebra and Geometry
38(1), 91 - 93 (1997)

Cutting Circles and the Morley Theorem

Ludwig Stammler

Fachbereich Mathematik und Informatik
Martin-Luther-Universita"t Halle-Wittenberg
Theodor-Lieser-Str. 5, D-06120 Halle

Abstract: For each triangle $ABC$ exist, additionally to the
circumscribed circle $c$, three and only three circles with the following
property: The circle cuts out of the lines ${\rm g}(BC)$, ${\rm g}(CA), {\rm g}(AB)$ chords of the length $BC, CA, AB$ respectively. Their midpoints are
the corners of an equilateral triangle, which is circumscribed about $c$
and has parallel sides to the Morley triangle. The proof is elementary (with
a trigonometrical calculation) and uses a property, also using for a known
proof of the Morley theorem.

Full text of the article:

Compressed DVI file (5074 Bytes)
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http://www.emc.dk/EMIS/journals/BAG/vol.38/no.1/7.html

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Antreas

Date Subject Author
9/12/98 Den Roussel
9/12/98 John Conway
9/13/98 Larry Cusick
10/27/98 John Conway
9/13/98 steve sigur
9/14/98 John Conway
9/15/98 John Conway
9/15/98 Richard Guy
9/15/98 John Conway
9/15/98 Richard Guy
9/15/98 Richard Guy
9/16/98 Floor van Lamoen
9/16/98 John Conway
9/17/98 Floor van Lamoen
9/17/98 John Conway
9/17/98 Floor van Lamoen
9/17/98 Russell Towle
9/17/98 John Conway
9/17/98 Russell Towle
9/17/98 Douglas J. Zare
9/19/98 Russell Towle
9/20/98 John Conway
9/20/98 John Conway
9/18/98 Antreas P. Hatzipolakis
11/10/98 Den Roussel