Answer: 1,121,252
Explanation:
First, we need to find the number of points of intersection of the chords inside the circle. To do this, we can use the formula for the number of intersection points in a circle formed by n chords, which is given by:
Number of intersection points = n(n - 1)/2
In this case, n = 1500, so:
Number of intersection points = 1500(1500 - 1)/2
Number of intersection points = 1500 * 1499/2
Number of intersection points = 750 * 1499
Number of intersection points = 1,124,250
Now, let's find the number of polygons formed by the chords inside the circle. When n chords intersect inside a circle, they form (n - 2) triangles and n non-triangle polygons. In this case, n = 1500, so:
Number of triangles = (1500 - 2) = 1498
Number of non-triangle polygons = 1500
Now, calculate the total number of polygons:
Total number of polygons = Number of triangles + Number of non-triangle polygons
Total number of polygons = 1498 + 1500
Total number of polygons = 2998
The difference between the number of points of intersection of the chords and the number of polygons formed by the chords inside the circle is:
Difference = Number of intersection points - Total number of polygons
Difference = 1,124,250 - 2998
Difference = 1,121,252
So, the difference between the number of points of intersection of the chords and the number of polygons formed by the chords inside the circle is 1,121,252.