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MAA AMC
AMC 12/AHSME
1966 AMC 12/AHSME
11
Angle Bisector
Angle Bisector
Source:
March 21, 2006
ratio
geometry
angle bisector
Problem Statement
The sides of triangle
B
A
C
BAC
B
A
C
are in the ratio
2
:
3
:
4
2: 3: 4
2
:
3
:
4
.
B
D
BD
B
D
is the angle-bisector drawn to the shortest side
A
C
AC
A
C
, dividing it into segments
A
D
AD
A
D
and
C
D
CD
C
D
. If the length of
A
C
AC
A
C
is
10
10
10
, then the length of the longer segment of
A
C
AC
A
C
is:
(A)
3
1
2
(B)
5
(C)
5
5
7
(D)
6
(E)
7
1
2
\text{(A)} \ 3\frac12 \qquad \text{(B)} \ 5 \qquad \text{(C)} \ 5\frac57 \qquad \text{(D)} \ 6 \qquad \text{(E)} \ 7\frac12
(A)
3
2
1
(B)
5
(C)
5
7
5
(D)
6
(E)
7
2
1
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