
Re: A Theorem concerning the Trisectors of a Triangle
Posted:
Sep 18, 1998 9:09 PM



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 MartinLutherUniversita"t HalleWittenberg TheodorLieserStr. 5, D06120 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.
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http://www.emc.dk/EMIS/journals/BAG/vol.38/no.1/7.html

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