Please help me with a reference or a proof for the following:
Find $n$ such that any convex polygon with $100$ sides can be obtained as an intersection of $n$ triangles.
First, $n \geq 34 $ since if the polygon is the intersection of $n$ triangles, each of the $100$ sides of the polygon must be contained in at least one of the triangles, therefore $3n \geq 100$. Now, I must prove that $n=34$, i.e. any polygon with 100 sides can be obtained intersecting $34$ triangles. These triangles should be formed by extending some sides of the polygon. The only problem would be that there is possible that three sides of the polygon form a triangle which does not contain the polygon, or do not form a triangle at all (if two sides are parallel).
Please help me with a reference or proof. Thank you.