Each pair intersect in 2 points.
The first circle intersects 9 others.
The 2nd circle intersects 8 others (not counting its intersections with the first circle)
The 3rd circle intersects 7 others (not counting its intersections with the first two)
....
The 9th circle intersects 1 other (not counting ...etc)
The 10th circle already intersects all the others.
Hence number of intersection points = 2*(9+8+7+6+5+4+3+2+1) = 2*45 = 90.