MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
1998 National Olympiad First Round
25
25
Part of
1998 National Olympiad First Round
Problems
(1)
P inside ABC
Source: 0
4/23/2009
In triangle
A
B
C
ABC
A
BC
with
∣
B
C
∣
>
∣
B
A
∣
\left|BC\right|>\left|BA\right|
∣
BC
∣
>
∣
B
A
∣
,
D
D
D
is a point inside the triangle such that \angle ABD\equal{}\angle DBC, \angle BDC\equal{}150{}^\circ and \angle DAC\equal{}60{}^\circ. What is the measure of
∠
B
A
D
\angle BAD
∠
B
A
D
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
45
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
50
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
60
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
75
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
80
<span class='latex-bold'>(A)</span>\ 45 \qquad<span class='latex-bold'>(B)</span>\ 50 \qquad<span class='latex-bold'>(C)</span>\ 60 \qquad<span class='latex-bold'>(D)</span>\ 75 \qquad<span class='latex-bold'>(E)</span>\ 80
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
45
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
50
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
60
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
75
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
80
geometry
angle bisector