A regular 13-gon is given. Diagonals [i]AC[/i], [i]BF[/i] and [i]BH[/i] are drawn. Intersection points [i]N[/i] and [i]O[/i] are defined as shown in the figure.[br]Prove that[br][list][*][i]a[/i]=[i]b[/i],[/*][*][i]a[/i]+[i]c[/i]=[i]d[/i].[/*][/list]

Given a regular (2[i]n[/i]-1)-gon (eventually a star-polygon), [i]n[/i]≥2. Let its vertices be labeled by numbers 0, 1, 2, ..., 2[i]n[/i]-1. Draw diagonals connecting vertices 0 and 2, and 1 and ([i]n[/i]+1), respectively. Draw the intersection point [i]P[/i] of these diagonals. Now the segment [i]P[/i]0 will be of the same length as the side of the regular polygon, that is, [i]P[/i]01 is an isosceles triangle.[br](This statement can be easily proven by computing the external angles of a polygon.)