Question

$\text{ABCD is a parallelogram with diagonal}\text{AC. If a line XY is drawn such that it cuts}\text{the side AD at point Z and XY || AB, then}\frac{BX}{XC}\text{can be equal to:}$

• A. $\frac{AY}{AC}$
• B. $\frac{DZ}{AZ}$
• C. $\frac{AZ}{ZD}$
• D. $\frac{AY}{YC}$

Answer 1

Answer: (C), (D)

The correct options are
C

$\frac{AZ}{ZD}$

D

$\frac{AY}{YC}$

$\text{Consider}\Delta ABC,$

$AB\parallel XY$

$\therefore \frac{BX}{XC}=\frac{AY}{YC}...\left(i\right)\text{(By Basic proportionality theorem)}$

$\text{Consider parallelogram ABCD,}AB||CD\text{(Opposite sides of a parallelogram are}\text{parallel)}$

$\Rightarrow AB\parallel CD\parallel XZ$

$\text{Consider}\Delta ACD,$

$CD\parallel YZ$

$\therefore \frac{AY}{YC}=\frac{AZ}{ZD}...\left(ii\right)\text{(By Basic proportionality theorem)}$

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