MathDB

10

Part of 2000 Moldova Team Selection Test

Problems(1)

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

Source: Moldova TST 2000

8/7/2023
Convex polygon A1A2…AnA_1A_2\ldots A_n is called balancedbalanced if there is a point MM{} inside it such that the half lines (AiM,(i=1,2,…,n)(A_iM, (i=1,2,\ldots,n) intersect disctinct sides of the polygon. a) Show that if n>3n>3 is even, then every polygon with nn{} sides is not balanced. b) Do polygons with an odd number of sides that are not balanced exist?
geometry