Would anyone be able to help me with the following problem or give me a push in the right direction? I am not entirely sure where to start and I have been looking at this problem for hours... Any help is appreciated.
Let n ≥ 3. Suppose an n- sided convex polygon is formed by taking n points on a circle, and joining adjacent points by straight lines. A diagonal of such a polygon is a straight line between two corners, that is not one of the sides of the original polygon.
Prove that the maximum number of diagonals that can be drawn in such a convex n- sided polygon, so that no two diagonals meet except at a corner, is n - 3.