About diagonals
Source: http://www.olimpiadamatematica.es/platea.pntic.mec.es/_csanchez/olimp_1963-2004/OME2004.pdf
November 14, 2016
geometrycombinatorics
Problem Statement
A convex polygon of sides is considered. All its diagonals are drawn and we suppose that any three of them can only intersect on a vertex and that there is no pair of parallel diagonals. Under these conditions, we wish to computea) The total number of intersection points of these diagonals, excluding the vertices.b) How many points, of these intersections, lie inside the polygon and how many lie outside.