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National and Regional Contests
Iran Contests
Iran MO (1st Round)
2018 Iran MO (1st Round)
10
10
Part of
2018 Iran MO (1st Round)
Problems
(1)
Find the length of CN in triangle ABC - Iran First Round 2018, P10
Source:
3/7/2021
Consider a triangle
A
B
C
ABC
A
BC
in which
A
B
=
A
C
=
15
AB=AC=15
A
B
=
A
C
=
15
and
B
C
=
18
BC=18
BC
=
18
. Points
D
D
D
and
E
E
E
are chosen on
C
A
CA
C
A
and
C
B
CB
CB
, respectively, such that
C
D
=
5
CD=5
C
D
=
5
and
C
E
=
3
CE=3
CE
=
3
. The point
F
F
F
is chosen on the half-line
D
E
ā
\overrightarrow{DE}
D
E
so that
E
F
=
8
EF=8
EF
=
8
. If
M
M
M
is the midpoint of
A
B
AB
A
B
and
N
N
N
is the intersection of
F
M
FM
FM
and
B
C
BC
BC
, what is the length of
C
N
CN
CN
?
geometry