In , two distinct lines each parallel to intersect and . The line nearer to meets at…

MATHEMATICS · Single correct · CBSE · Mathematics · Triangles · Triangles

Problem

\triangle ABC

, two distinct lines each parallel to

BC

intersect

AB

and

AC

. The line nearer to

BC

meets

AB

D

and

AC

E

, while the line nearer to

A

meets

AB

F

and

AC

G

(with

F

between

A

and

D

). Given

AD = 6\,\text{cm}

DB = 12\,\text{cm}

AF = 4\,\text{cm}

and

AG = 5\,\text{cm}

, find the length of

GC

. (a)

15.5\ \text{cm}

(b)

19.5\ \text{cm}

(c)

17.5\ \text{cm}

(d)

21.5\ \text{cm}