Repeated angles in the plane and related problems
János Pach, Micha Sharir · Journal of Combinatorial Theory Series A · 1992
We show that a set of n points in the plane determine O(n2 log n) triples that define the same angle α, and that for many angles α (including π2) this bound is tight in the worst case. We also show that, for a broad family of properties P, the number of triangles spanned by the given points and having property P is O(n73). Typical such properties are: having a specified area, a specified perimeter, being isosceles, etc.