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Math Help - Diagonal

  1. #1
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    Exclamation 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?
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  2. #2
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    Quote Originally Posted by vivian View Post
    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: \frac n2 \cdot (n-3)

    Each diagonal is intersected by (n-3) diagonals. Therefore the number of intersections is: \frac n2 \cdot (n-3)^2

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