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Nordic
2000 Nordic
3
3
Part of
2000 Nordic
Problems
(1)
isosceles or <A = 60^o, because of angle bisectors
Source: Nordic Mathematical Contest 2000 #3
10/3/2017
In the triangle
A
B
C
ABC
A
BC
, the bisector of angle
∠
B
\angle B
∠
B
meets
A
C
AC
A
C
at
D
D
D
and the bisector of angle
∠
C
\angle C
∠
C
meets
A
B
AB
A
B
at
E
E
E
. The bisectors meet each other at
O
O
O
. Furthermore,
O
D
=
O
E
OD = OE
O
D
=
OE
. Prove that either
A
B
C
ABC
A
BC
is isosceles or
∠
B
A
C
=
6
0
∘
\angle BAC = 60^\circ
∠
B
A
C
=
6
0
∘
.
geometry
isosceles
angle bisector