MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1957 AMC 12/AHSME
50
50
Part of
1957 AMC 12/AHSME
Problems
(1)
The Path of Point O'
Source:
6/8/2009
In circle
O
O
O
,
G
G
G
is a moving point on diameter
A
B
‾
\overline{AB}
A
B
.
A
A
′
‾
\overline{AA'}
A
A
′
is drawn perpendicular to
A
B
‾
\overline{AB}
A
B
and equal to
A
G
‾
\overline{AG}
A
G
.
B
B
′
‾
\overline{BB'}
B
B
′
is drawn perpendicular to
A
B
‾
\overline{AB}
A
B
, on the same side of diameter
A
B
‾
\overline{AB}
A
B
as
A
A
′
‾
\overline{AA'}
A
A
′
, and equal to
B
G
BG
BG
. Let
O
′
O'
O
′
be the midpoint of
A
′
B
′
‾
\overline{A'B'}
A
′
B
′
. Then, as
G
G
G
moves from
A
A
A
to
B
B
B
, point
O
′
O'
O
′
:
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
moves on a straight line parallel to
A
B
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
remains stationary
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
moves on a straight line perpendicular to
A
B
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
moves in a small circle intersecting the given circle
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
follows a path which is neither a circle nor a straight line
<span class='latex-bold'>(A)</span>\ \text{moves on a straight line parallel to }{AB}\qquad \\ <span class='latex-bold'>(B)</span>\ \text{remains stationary}\qquad \\ <span class='latex-bold'>(C)</span>\ \text{moves on a straight line perpendicular to }{AB}\qquad \\ <span class='latex-bold'>(D)</span>\ \text{moves in a small circle intersecting the given circle}\qquad \\ <span class='latex-bold'>(E)</span>\ \text{follows a path which is neither a circle nor a straight line}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
moves on a straight line parallel to
A
B
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
remains stationary
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
moves on a straight line perpendicular to
A
B
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
moves in a small circle intersecting the given circle
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
follows a path which is neither a circle nor a straight line