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From: trough@ihuxa.UUCP (Chris Scussel)
Newsgroups: net.math
Subject: Generalizations of Morley's Theorem
Message-ID: <341@ihuxa.UUCP>
Date: Thu, 1-Dec-83 14:20:21 EST
Article-I.D.: ihuxa.341
Posted: Thu Dec  1 14:20:21 1983
Date-Received: Sat, 3-Dec-83 12:18:15 EST
Organization: AT&T Bell Labs, Naperville, Il
Lines: 13

Morley's theorem state that the intersections of the (correct) pairs of
a triangle's angle trisectors are the vertices of an equilateral triangle.
The bisectors meet at a point (one of the many "special" points of a triangle).
Now consider an x-sector: a line that "cuts off" the proportion x of the
angle (e.g., a bisector has x=1/2, a trisector has x=1/3). Now consider what
happens as x varies. Note that when x=0 the x-sectors are collinear, but
intersection points are still well defined (as limits). What other
values of x are interesting besides 0, 1/2, and 1/3? What about extending
the domain of x beyond [0,1/2]? Comments?

				Chris Scussel
				Bell Labs
				Naperville, Ill.