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no of diagonals, in polygons by a diagonal in 100-gon 1987 Greece MO Grade X p4

Source:

September 6, 2024
geometrycombinatoricscombinatorial geometry

Problem Statement

Consider a convex 100100-gon A1A2...A100A_1A_2...A_{100}. Draw the diagonal A43A81A_{43}A_{81} which divides it into two convex polygons P1,P2P_1,P_2. How many vertices and how diagonals, has each of the polygons P1,P2P_1,P_2?
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