Given the nine-sided regular polygon A1A2A3A4A5A6A7A8A9, how many distinct equilateral triangles in the plane of the polygon have at least two vertices in the set { A1, A2, A3,.........A9 } ?

I think I am not understanding the problem correctly. I could only come up with 36, but the answer is 66.

Vicky(Headbang)