Question

Point E bisects side CD of a parallelogram ABCD and CF intersects DA produced at G such that $CF||AE$, where F is a point on AB. The value of $AD\times GF–CF\times AG$ is

• A. 4
• B. 0
• C. 1
• D. 2

Answer 1

The correct option is B 0


Given: $AE||CF$ and $ED=EC$
In $\Delta CDG$, by the converse of mid-point theorem,
A will be the mid-point of DG.
$\Rightarrow AD=AG$ …..(i)
Also, $AE=\frac{1}{2}GC$
Also, in $\Delta GCD$,
A is the mid-point of $GD$ and $AF||CD$ (as ABCD is a parallelogram)
$\therefore$ By converse of mid-point theorem F will be the mid-point of GC
$\Rightarrow GF=CF$ ….(ii)
$\therefore AD\times GF–CF\times AG=AG\times CF–CF\times AG$ [From (i) and (ii)]
$=0$
Hence, the correct answer is option (b).