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National and Regional Contests
Turkey Contests
Turkey Junior National Olympiad
2004 Turkey Junior National Olympiad
1
1
Part of
2004 Turkey Junior National Olympiad
Problems
(1)
Turkey Junior Olympiad 2004, Part II - P1
Source:
1/20/2013
Let
[
A
D
]
[AD]
[
A
D
]
and
[
C
E
]
[CE]
[
CE
]
be internal angle bisectors of
△
A
B
C
\triangle ABC
△
A
BC
such that
D
D
D
is on
[
B
C
]
[BC]
[
BC
]
and
E
E
E
is on
[
A
B
]
[AB]
[
A
B
]
. Let
K
K
K
and
M
M
M
be the feet of perpendiculars from
B
B
B
to the lines
A
D
AD
A
D
and
C
E
CE
CE
, respectively. If
∣
B
K
∣
=
∣
B
M
∣
|BK|=|BM|
∣
B
K
∣
=
∣
BM
∣
, show that
△
A
B
C
\triangle ABC
△
A
BC
is isosceles.
geometry
incenter