MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2001 National Olympiad First Round
13
13
Part of
2001 National Olympiad First Round
Problems
(1)
P13 [Geometry] - Turkish NMO 1st Round - 2001
Source:
4/20/2014
Let
A
B
C
ABC
A
BC
be a triangle such that
∣
B
C
∣
=
7
|BC|=7
∣
BC
∣
=
7
and
∣
A
B
∣
=
9
|AB|=9
∣
A
B
∣
=
9
. If
m
(
A
B
C
^
)
=
2
m
(
B
C
A
^
)
m(\widehat{ABC}) = 2m(\widehat{BCA})
m
(
A
BC
)
=
2
m
(
BC
A
)
, then what is the area of the triangle?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
14
5
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
30
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
10
6
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
20
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
12
3
<span class='latex-bold'>(A)</span>\ 14\sqrt 5 \qquad<span class='latex-bold'>(B)</span>\ 30 \qquad<span class='latex-bold'>(C)</span>\ 10\sqrt 6 \qquad<span class='latex-bold'>(D)</span>\ 20 \sqrt 2 \qquad<span class='latex-bold'>(E)</span>\ 12 \sqrt 3
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
14
5
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
30
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
10
6
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
20
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
12
3
geometry
trigonometry