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Olympic Revenge
2008 Olympic Revenge
2008 Olympic Revenge
Part of
Olympic Revenge
Subcontests
(1)
1
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Another problem from Carlos Shine's notes(20th problem)
(Olympic Revenge 2008) Let
A
B
C
ABC
A
BC
be a triangle and
M
M
M
the midpoint of
B
C
BC
BC
. Let
D
D
D
and
E
E
E
be points such that
A
B
C
ABC
A
BC
,
D
B
A
DBA
D
B
A
and
E
A
C
EAC
E
A
C
are similar (in this order). The symmedians of
D
D
D
with respect to
D
B
A
DBA
D
B
A
and
E
E
E
with respect to
E
A
C
EAC
E
A
C
meet at
K
K
K
. Suppose that AM/BC=√3/2 Prove that
K
A
B
KAB
K
A
B
and
K
C
A
KCA
K
C
A
are similar (in this order).