Question 134264
One way to start thinking about it is to play around with a fewer number of
points, say 5 equally spaced around a circle. Label the points 1-5
Starting at point 1, draw lines to the other 4 points. You have 4 lines,
or (5 - 1). 
From point 2, draw lines to the other 4 points. You have 4 lines, but the 
line to point 1 was already there, so subtract 1.
So far you have
from point 1: (5 - 1)
from point 2: (5 - 1) - 1
From point 3 draw lines to the other 4 points. You have 4 lines, but the
lines to point 1 and point 2 were already there, so subtract 2
Now finish for all 5 points
from point 1: (5 - 1)
from point 2: (5 - 1) - 1
from point 3: (5 - 1) - 2
from point 4: (5 - 1) - 3
from point 5: (5 - 1) - 4
Doing the additions and subtractions , I get
{{{5*4 - 10 = 10}}} lines. I counted them- it works
Now I can come up with a formula for any number of points
arranged on a circle and use it for 15 points
Let {{{n}}} = the number of points 
Let {{{k}}} = the number of different lines connecting the points
{{{k = n*(n - 1)}}} - (the sum 1 + 2 + 3 + 4 + . . . + (n - 1))
There is a formula for the sum. It is {{{((n-1)/2)((n-1)+1)}}}
which simplifies to {{{(n*(n-1))/2}}}
So far, the formula is
{{{k = n*(n-1) - n*(n-1)/2}}}
{{{k = n*(n-1)/2}}} general formula
Now see if this formula works for 5 points
{{{k = 5*(5-1)/2}}}
{{{k = 10}}} It works
Now for 15 points
{{{k = 15*14/2}}}
{{{k = 105}}} answer
Hope this didn't confuse you
The general formula should work for any number of points