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 shape with 25 vertices, all the diagonals are drawn.
Prove that there are no nine diagonals passing through one interior point of the shape.