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Turkey Junior National Olympiad
2000 Turkey Junior National Olympiad
1
1
Part of
2000 Turkey Junior National Olympiad
Problems
(1)
Turkey Junior Olympiad 2000, Part II - P1
Source:
1/18/2013
Let
A
B
C
ABC
A
BC
be a triangle with
∠
B
A
C
=
9
0
∘
\angle BAC = 90^\circ
∠
B
A
C
=
9
0
∘
. Construct the square
B
D
E
C
BDEC
B
D
EC
such as
A
A
A
and the square are at opposite sides of
B
C
BC
BC
. Let the angle bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
cut the sides
[
B
C
]
[BC]
[
BC
]
and
[
D
E
]
[DE]
[
D
E
]
at
F
F
F
and
G
G
G
, respectively. If
∣
A
B
∣
=
24
|AB|=24
∣
A
B
∣
=
24
and
∣
A
C
∣
=
10
|AC|=10
∣
A
C
∣
=
10
, calculate the area of quadrilateral
B
D
G
F
BDGF
B
D
GF
.
geometry
angle bisector