MathDB

convex polygon is divided into some triangles, set of vertices and edges

Source: 2017 Saudi Arabia IMO Training Test p6

September 4, 2020

combinatorial geometrycombinatoricsconvex

Problem Statement

A convex polygon is divided into some triangles. Let

V

and

E

be respectively the set of vertices and the set of egdes of all triangles (each vertex in

V

may be some vertex of the polygon or some point inside the polygon). The polygon is said to be good if the following conditions hold: i. There are no

3

vertices in

V

which are collinear. ii. Each vertex in

V

belongs to an even number of edges in

E

. Find all good polygon.