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Concurrent Diagonals in a 30-Gon

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select triple
102
rotate lines
-13
When three lines meet at a point, they are concurrent. For the diagonals of a 30-gon, out of the 16801 intersection points, there are 3001 points where three or more lines intersect, with 193 different ways to select three concurrent diagonals.
Consider six points that divide a circle into arcs
(abcdef)
. If
sin
a
2
sin
c
2
sin
e
2
=sin
b
2
sin
d
2
sin
f
2
, then the three lines connecting opposing points are concurrent [1]. This property was used to find the sets of lines. By the pizza theorem, half the circle is covered by wedges
ace
, and half by wedges
bdf
.
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