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Mathematics
Mathematics
Problem
Given an equilateral
△
A
B
C
\triangle ABC
△
A
B
C
with side length equal to
a
a
a
. Let
M
M
M
and
N
N
N
be two points respectively, on the side
A
B
AB
A
B
and
A
C
AC
A
C
such that
A
N
=
k
A
C
AN = kAC
A
N
=
k
A
C
and
A
M
=
A
B
3
AM = \frac{AB}{3}
A
M
=
3
A
B
. If
B
N
\mathbf{BN}
BN
and
C
M
\mathbf{CM}
CM
are orthogonal, then the value of
k
k
k
is a.
1
5
\frac{1}{5}
5
1
b.
1
4
\frac{1}{4}
4
1
c.
1
3
\frac{1}{3}
3
1
d.
1
2
\frac{1}{2}
2
1
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