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2016 ASDAN Math Tournament
8
2016 Team #8
2016 Team #8
Source:
August 17, 2022
2016
team test
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
=
24
AB=24
A
B
=
24
,
B
C
=
30
BC=30
BC
=
30
, and
A
C
=
36
AC=36
A
C
=
36
. Point
M
M
M
lies on
B
C
BC
BC
such that
B
M
=
12
BM=12
BM
=
12
, and point
N
N
N
lies on
A
C
AC
A
C
such that
C
N
=
20
CN=20
CN
=
20
. Let
X
X
X
be the intersection of
A
M
AM
A
M
and
B
N
BN
BN
and let line
C
X
CX
CX
intersect
A
B
AB
A
B
at point
L
L
L
. Compute
A
X
X
M
+
B
X
X
N
+
C
X
X
L
.
\frac{AX}{XM}+\frac{BX}{XN}+\frac{CX}{XL}.
XM
A
X
+
XN
BX
+
X
L
CX
.
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