Question

$ABCD$ is a parallelogram with diagonal $AC$. If a line $XZ$ is drawn such that $XZ\parallel AB$ and cuts $AC$ at $Y$ then, find$\frac{BX}{XC}.$

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

Answer 1

The correct option is A

$\frac{AZ}{ZD}$

In the $\Delta$ ABC,

$AB\parallel XZ$

$\Rightarrow AB\parallel XY$

$\therefore$ $\frac{BX}{XC}=\frac{AY}{YC}....\left(1\right)$ [By Basic Proportionality Theorem]

In parallelogram ABCD,
AB $\parallel$ CD

AB $\parallel$ CD $\parallel$ XZ

In the $\Delta$ ACD,
CD $\parallel$ YZ

$\therefore$ $\frac{AY}{YC}=\frac{AZ}{ZD}....\left(2\right)$ [By Basic Proportionality Theorem]

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

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