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Find the length of CN in triangle ABC - Iran First Round 2018, P10

Source:

March 7, 2021

geometry

Problem Statement

Consider a triangle

ABC

in which

AB=AC=15

and

BC=18

. Points

D

and

E

are chosen on

CA

and

CB

, respectively, such that

CD=5

and

CE=3

. The point

F

is chosen on the half-line

\overrightarrow{DE}

so that

EF=8

. If

M

is the midpoint of

AB

and

N

is the intersection of

FM

and

BC

, what is the length of

CN

?

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