Problems

We create some segments in a regular $n$-gon by joining endpoints of the $n$-gon. What’s the maximum number of such segments while ensuring that no two segments are parallel? The segments are allowed to be sides of the $n$-gon - that is, joining adjacent vertices of the polygon.

In a regular polygon with $25$ vertices, all the diagonals are drawn.

Prove that there are no nine diagonals passing through one interior point of the shape.