MathDB

Midpolygon perimeter

Source: Canada Repêchage 2016/5

June 19, 2016

geometrycombinatoricsCanada

Problem Statement

Consider a convex polygon

P

with

n

sides and perimeter

P_0

. Let the polygon

Q

, whose vertices are the midpoints of the sides of

P

, have perimeter

P_1

. Prove that

P_1 \geq \frac{P_0}{2}