MathDB

2010 smo (5)

Source: 2010 China South East Mathematical Olympiad

July 18, 2011

inequalitiesgeometry unsolvedgeometry

Problem Statement

ABC

is a triangle with a right angle at

C

M_1

and

M_2

are two arbitrary points inside

ABC

, and

M

is the midpoint of

M_1M_2

. The extensions of

BM_1,BM

and

BM_2

intersect

AC

N_1,N

and

N_2

respectively. Prove that

\frac{M_1N_1}{BM_1}+\frac{M_2N_2}{BM_2}\geq 2\frac{MN}{BM}