Solution

We can get the triangles in two different ways.

Taking two points from the line having 10 points

(in ¹⁰C2 ways, i.e., 45 ways) and one point from the line consisting of 11 points (in 11 ways).

So, the number of triangles here is 45×11=495.

Taking two points from the line having 11 points (in ¹¹C2, i.e., 55 ways) and one point from the line consisting of 10 points (in 10 ways), the number of triangles here is 55×10=550

Total number of triangles, =495+550

=1,045 triangles