MathDB

perimeter of A'B'C' less than k times the perimeter of ABC

Source: 1952 Hungary - Kürschák Competition p3

October 10, 2022

geometryperimeterGeometric Inequalitiesratio

Problem Statement

ABC

is a triangle. The point A' lies on the side opposite to

A

and

BA'/BC = k

, where

1/2 < k < 1

. Similarly,

B'

lies on the side opposite to

B

with

CB'/CA = k

, and

C'

lies on the side opposite to

C

with

AC'/AB = k

. Show that the perimeter of

A'B'C'

is less than

k

times the perimeter of

ABC