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National and Regional Contests
India Contests
Regional Mathematical Olympiad
2001 India Regional Mathematical Olympiad
1
1
Part of
2001 India Regional Mathematical Olympiad
Problems
(1)
Another parallel
Source: Indian RMO 2001 Problem 1
10/27/2005
Let
B
E
BE
BE
and
C
F
CF
CF
be the altitudes of an acute triangle
A
B
C
ABC
A
BC
with
E
E
E
on
A
C
AC
A
C
and
F
F
F
on
A
B
AB
A
B
. Let
O
O
O
be the point of intersection of
B
E
BE
BE
and
C
F
CF
CF
. Take any line
K
L
KL
K
L
through
O
O
O
with
K
K
K
on
A
B
AB
A
B
and
L
L
L
on
A
C
AC
A
C
. Suppose
M
M
M
and
N
N
N
are located on
B
E
BE
BE
and
C
F
CF
CF
respectively. such that
K
M
KM
K
M
is perpendicular to
B
E
BE
BE
and
L
N
LN
L
N
is perpendicular to
C
F
CF
CF
. Prove that
F
M
FM
FM
is parallel to
E
N
EN
EN
.