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n-Sectors of the Angles of a Triangle

​
kind of triangle
angle divisions n
2
show lines
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○
equilateral
intersections of lines from
A
or
B
or
C
: 1
The
n
-sectors of an angle are the lines that divide the angle into
n
equal parts. In a triangle, the bisectors are collinear, the trisectors lead to Morley's theorem, …. More modestly, this Demonstration provides a way to count the intersection points of the
n
-sectors of the angles of a triangle as a function of
n
, which is
3
2
n
-6n-
n
(-1)
+2
for a scalene triangle.
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