MathDB

h<=2H , altitudes inequality of an acute triangle inscribed in a triangle

Source: 2007 Balkan Shortlist BMO G4 - Bulgaria

April 5, 2020

geometric inequalityaltitudesaltitudegeometry

Problem Statement

Points

M,N

and

P

on the sides

BC, CA

and

AB

\vartriangle ABC

are such that

\vartriangle MNP

is acute. Denote by

h

and

H

the lengths of the shortest altitude of

\vartriangle ABC

and the longest altitude of

\vartriangle MNP

. Prove that

h \le 2H