Question

In the following figure, $XY$ is parallel to $BC$, $AX=9$ cm, $XB=4.5$ cm and $BC=18$ cm. Find $\frac{AY}{YC}$

• A. $1$
• B. $4$
• C. $3$
• D. $2$

Answer 1

The correct option is D $2$

In $△AXY$ and $△ABC$
$\angle XAY=\angle BAC$ (Common angle)
$\angle AXY=\angle ABC$ (Corresponding angles for parallel lines $XY$ and $BC$)
$\angle AYX=\angle ACB$ (Corresponding angles for parallel lines $XY$ and $BC$)
Thus, $△AXY\sim △ABC$ (AAA rule)
Hence, $\frac{AB}{AX}=\frac{AC}{AY}$ (Corresponding sides)
On subtracting $1$ from both the sides, we have

$\frac{AB}{AX}-1=\frac{AC}{AY}-1$

$\Rightarrow \frac{AB-AX}{AX}=\frac{AC-AY}{AY}$

$\Rightarrow \frac{XB}{AX}=\frac{YC}{AY}$

$\Rightarrow \frac{4.5}{9}=\frac{YC}{AY}$

$\Rightarrow \frac{AY}{YC}=2$