Problem 54020. Circle Division

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A circle can be divided into 2 sections, by placing 2 points in arbitrary locations along its circumference and drawing a straight line between them. By adding more points and drawing a straight line from each point to every other point, the circle can be divided into more sections. For example, 3 points would divide the circle into 4 sections and 4 points into 8 sections.
Given a positive integer, n, representing the number of arbitrarily placed points on the circumference of a circle, return d, i and s, the number of straight lines, the number of intersections and the number of sections into which the circle is divided, respectively.
The only restriction on the positions of the points is that they must be placed such that no 3 lines can share a single intersection.
n will always be greater than 3.
Example:
n = 4;
d = 6
i = 1
s = 8
Example:
n = 5;
d = 10
i = 5
s = 16