MathDB
Problems
Contests
International Contests
IMO Shortlist
1969 IMO Shortlist
57
57
Part of
1969 IMO Shortlist
Problems
(1)
Singapore Mathematical Olympiad 2009 Problem 1
Source:
8/3/2010
Given triangle
A
B
C
ABC
A
BC
with points
M
M
M
and
N
N
N
are in the sides
A
B
AB
A
B
and
A
C
AC
A
C
respectively. If
B
M
M
A
+
C
N
N
A
=
1
\dfrac{BM}{MA} +\dfrac{CN}{NA} = 1
M
A
BM
+
N
A
CN
=
1
, then prove that the centroid of
A
B
C
ABC
A
BC
lies on
M
N
MN
MN
.
geometry
Centroid
Triangle
IMO Shortlist
IMO Longlist