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JBMO ShortLists
2006 JBMO ShortLists
12
12
Part of
2006 JBMO ShortLists
Problems
(1)
Equilateral triangle and midpoints
Source: JBMO Shortlist 2006
11/10/2008
Let
A
B
C
ABC
A
BC
be an equilateral triangle of center
O
O
O
, and
M
ā
B
C
M\in BC
M
ā
BC
. Let
K
,
L
K,L
K
,
L
be projections of
M
M
M
onto the sides
A
B
AB
A
B
and
A
C
AC
A
C
respectively. Prove that line
O
M
OM
OM
passes through the midpoint of the segment
K
L
KL
K
L
.
geometry
parallelogram
geometry proposed