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MAA AMC
AMC 12/AHSME
1968 AMC 12/AHSME
11
11
Part of
1968 AMC 12/AHSME
Problems
(1)
Ratio of Areas Between Two Circles
Source: 1968 AHSME Problem #11
9/7/2011
If an arc of
6
0
∘
60^\circ
6
0
∘
on circle I has the same length as an arc of
4
5
∘
45^\circ
4
5
∘
on circle II, the ratio of the area of circle I to that of circle II is:
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
16
:
9
<
s
p
a
n
c
l
a
s
s
=
′
l
a
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e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
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>
9
:
16
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
4
:
3
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
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p
a
n
>
3
:
4
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
None of these
<span class='latex-bold'>(A)</span>\ 16:9 \qquad <span class='latex-bold'>(B)</span>\ 9:16 \qquad <span class='latex-bold'>(C)</span>\ 4:3 \qquad <span class='latex-bold'>(D)</span>\ 3:4 \qquad <span class='latex-bold'>(E)</span>\ \text{None of these}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
16
:
9
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
9
:
16
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
4
:
3
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
3
:
4
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
None of these
ratio
geometry
AMC