Triangles in a Hexagon
A convex hexagon is drawn together with all 9 of its diagonals, and no three diagonals pass through a common interior point. How many triangles (of any size) appear in the figure, i.e. triangles whose three sides each lie along drawn segments? Give an integer.
Related problems & prerequisites
Worth solving first
- Lines and Circles 5.0/10
- Crossings in a Regular Dodecagon 5.0/10
- Two Peaceful Queens 4.0/10
Source: Count of triangles formed by the sides and diagonals of a convex polygon in general position; classic in wide circulation. Statement written for AxiomIQ.