In , points and lie on and respectively such that . A second line is drawn inside to…

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

\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

F

and

AE

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. (i) Find the lengths of

AE

and

EC

. (ii) Calculate

FD

. (iii) Determine the lengths of

AG

and

GE