MathDB

Diagonal

AC

is drawn in rectangle

ABCD

. Points

E

and

F

are placed on

BC

such that

CE:EF:FB=2:1:1

. Let

G

be the intersection of

DF

with

AC

and

H

the intersection of

DE

with

AC

. Given that

AD=4

and

AB=8

, find the length of

GH

. Express your answer as a common fraction in simplest radical form.
https://cdn.artofproblemsolving.com/attachments/4/c/b69d79cd47bcb945e7a489533eb9761ccc7ccd.png

<span class='latex-bold'>(A) </span> \dfrac{4\sqrt5}{21}\qquad<span class='latex-bold'>(B) </span> \dfrac{8\sqrt5}{21}\qquad<span class='latex-bold'>(C) </span> \dfrac{10\sqrt5}{21}\qquad<span class='latex-bold'>(D) </span> \dfrac{4\sqrt5}{5}\qquad<span class='latex-bold'>(E) </span> \sqrt5

Problem Statement