How many triangles in picture?

Question

Can you tell me how many triangles are in this picture? I've counted 96, not sure that I got right answer.

Answer 1

Let's see! We'll break it up into the following cases (where an apex means one of the six points of the star):

A: Triangles that contain three apexes
There are 2 of these.

B: Triangles that contain a pair of opposite apexes
For each such pair, there are 2 of these, so 6 in total.

C: Triangles that contain a pair of non-opposite apexes
For each non-adjacent apex pair, there are three of these, so 18 in total.

D: Triangles that contain exactly one apex
For each apex, I count 10 such triangles, so 60 in total.

E: Triangles that contain no apex
For each edge of the internal hexagon, there are 3 triangles, so 18 in total.

I make that 2 + 6 + 18 + 60 + 18 = 104.

Answer 2

I only get 98. I am missing the 3rd triangle under section C. I only see 2 triangles that contain a pair of non-opposite apexes.