MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
2021 AMC 12/AHSME Fall
11
11
Part of
2021 AMC 12/AHSME Fall
Problems
(1)
What's PoPping?
Source: AMC 12A #11
11/11/2021
Consider two concentric circles of radius
17
17
17
and
19.
19.
19.
The larger circle has a chord, half of which lies inside the smaller circle. What is the length of the chord in the larger circle?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
12
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
10
3
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
17
⋅
19
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
18
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
8
6
<span class='latex-bold'>(A)</span>\ 12\sqrt{2} \qquad<span class='latex-bold'>(B)</span>\ 10\sqrt{3} \qquad<span class='latex-bold'>(C)</span>\ \sqrt{17 \cdot 19} \qquad<span class='latex-bold'>(D)</span>\ 18 \qquad<span class='latex-bold'>(E)</span>\ 8\sqrt{6}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
12
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
10
3
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
17
⋅
19
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
18
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
8
6
AMC
AMC 12
AMC 12 A