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India National Olympiad
2011 India National Olympiad
1
1
Part of
2011 India National Olympiad
Problems
(1)
D on BC, E on CA, F on AB such that BDF=CED=AFE -[INMO 2011]
Source:
2/6/2011
Let
D
,
E
,
F
D,E,F
D
,
E
,
F
be points on the sides
B
C
,
C
A
,
A
B
BC,CA,AB
BC
,
C
A
,
A
B
respectively of a triangle
A
B
C
ABC
A
BC
such that
B
D
=
C
E
=
A
F
BD=CE=AF
B
D
=
CE
=
A
F
and
∠
B
D
F
=
∠
C
E
D
=
∠
A
F
E
.
\angle BDF=\angle CED=\angle AFE.
∠
B
D
F
=
∠
CE
D
=
∠
A
FE
.
Show that
△
A
B
C
\triangle ABC
△
A
BC
is equilateral.
trigonometry
symmetry
geometry proposed
geometry