MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1962 AMC 12/AHSME
23
23
Part of
1962 AMC 12/AHSME
Problems
(1)
Length of a Segment
Source:
3/3/2010
In triangle
A
B
C
ABC
A
BC
,
C
D
CD
C
D
is the altitude to
A
B
AB
A
B
and
A
E
AE
A
E
is the altitude to
B
C
.
BC.
BC
.
If the lengths of
A
B
,
C
D
,
AB, CD,
A
B
,
C
D
,
and
A
E
AE
A
E
are known, the length of
D
B
DB
D
B
is:
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
not determined by the information given
<span class='latex-bold'>(A)</span>\ \text{not determined by the information given} \qquad
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
not determined by the information given
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
determined only if A is an acute angle
<span class='latex-bold'>(B)</span>\ \text{determined only if A is an acute angle} \qquad
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
determined only if A is an acute angle
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
determined only if B is an acute angle
<span class='latex-bold'>(C)</span>\ \text{determined only if B is an acute angle} \qquad
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
determined only if B is an acute angle
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
determined only in ABC is an acute triangle
<span class='latex-bold'>(D)</span>\ \text{determined only in ABC is an acute triangle} \qquad
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
determined only in ABC is an acute triangle
<
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 is correct
<span class='latex-bold'>(E)</span>\ \text{none of these is correct}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
none of these is correct