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National and Regional Contests
Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2004 Bosnia and Herzegovina Junior BMO TST
5
5
Part of
2004 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
D belongs to the angle bisector of <AGF
Source: 2004 Bosnia & Herzegovina JBMO TST p5
5/27/2020
In the isosceles triangle
A
B
C
ABC
A
BC
(
A
C
=
B
C
AC = BC
A
C
=
BC
),
A
B
=
3
AB =\sqrt3
A
B
=
3
and the altitude
C
D
=
2
CD =\sqrt2
C
D
=
2
. Let
E
E
E
and
F
F
F
be the midpoints of
B
C
BC
BC
and
D
B
DB
D
B
, respectively and
G
G
G
be the intersection of
A
E
AE
A
E
and
C
F
CF
CF
. Prove that
D
D
D
belongs to the angle bisector of
∠
A
G
F
\angle AGF
∠
A
GF
.
isosceles
angle bisector
geometry