Thread: Diagonal

Consider a convex n-gon such that no 3 diagonals intersect at a single point. Draw all the diagonals (i.e. connect every pair of vertices by a segment).

a) How many intersections do the diagonals determine?

b) Into how many parts is the polygon divided by the diagonals?

Originally Posted by vivian

Consider a convex n-gon such that no 3 diagonals intersect at a single point. Draw all the diagonals (i.e. connect every pair of vertices by a segment).

a) How many intersections do the diagonals determine?

b) Into how many parts is the polygon divided by the diagonals?

Hello,

to a). from each vertex there are starting (n-3) diagonals.

The total number of diagonals is therefore:

Each diagonal is intersected by (n-3) diagonals. Therefore the number of intersections is:

to b) I'm not quite sure what you mean by parts