Mathematics

Mathematics

Problem

In

\triangle ABC

, points

D

and

E

lie on

AB

and

AC

respectively such that

DE\parallel BC

. A second line

FG

is drawn inside

\triangle ADE

to meet

AD

at

F

and

AE

at

G

, with

FG\parallel DE

. Given

AD = 4\,\text{cm}

,

DB = 8\,\text{cm}

,

AC = 18\,\text{cm}

and

AF = 3\,\text{cm}

, answer the following questions. a. (i) Find the lengths of

AE

and

EC

. b. (ii) Calculate

FD

. c. (iii) Determine the lengths of

AG

and

GE

.

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