MathDB

Grade IX - Problem II

Source: Romanian National Mathematical Olympiad 2007

April 14, 2007

geometrygeometry unsolved

Problem Statement

Let

ABC

be an acute angled triangle and point

M

chosen differently from

A,B,C

. Prove that

M

is the orthocenter of triangle

ABC

if and only if

\frac{BC}{MA}\vec{MA}+\frac{CA}{MB}\vec{MB}+\frac{AB}{MC}\vec{MC}= \vec{0}