Question

ABCD is a parallelogram with diagonal AC. If a line XY is drawn such that XZ $\parallel$ AB then $\frac{BX}{XC}$ =?

• A. AY/AC
• B. DZ/AZ
• C. AZ/ZD
• D. AC/AY

Answer 1

The correct option is C

AZ/ZD

In parallelogram ABCD,
AB $\parallel$ CD
AB $\parallel$ CD $\parallel$ XZ

In $\Delta$ ABC,
AB $\parallel$ XZ
$\Rightarrow$ AB $\parallel$ XY
$\therefore$ $\frac{BX}{XC}$ = $\frac{AY}{YC}$ ..... (1) [By BPT]

In $\Delta$ ACD,
CD $\parallel$ YZ
$\therefore$ $\frac{AY}{YC}$ = $\frac{AZ}{ZD}$ ...... (2) [By BPT]

From (1) and (2),
$\frac{BX}{XC}$ = $\frac{AY}{YC}$ = $\frac{AZ}{ZD}$

$\frac{BX}{XC}$ = $\frac{AZ}{ZD}$