MathDB

there is a point $M$ inside it such that the half lines $(A_iM, i=1,2,\ldots,n$

Source: Moldova TST 2000

August 7, 2023

geometry

Problem Statement

Convex polygon

A_1A_2\ldots A_n

is called

balanced

if there is a point

M{}

inside it such that the half lines

(A_iM, (i=1,2,\ldots,n)

intersect disctinct sides of the polygon. a) Show that if

n>3

is even, then every polygon with

n{}

sides is not balanced. b) Do polygons with an odd number of sides that are not balanced exist?