Question

In the given figure, $XY\parallel BC$ and $XZ\parallel AC$, then $\frac{AX}{AB}=$

• A. $\frac{XZ}{AB}$
• B. $\frac{XY}{AC}$
• C. $\frac{CZ}{BC}$
• D. $\frac{BZ}{BC}$

Answer 1

Answer: (C)

$\frac{CZ}{BC}$

Given : $XY\parallel BC$ and $XZ\parallel AC$

$⟹$ $\frac{AX}{XB}=\frac{AY}{YC}$ and $\frac{XB}{AX}=\frac{ZB}{CZ}$ ..................... $\left(1\right)$

Consider, $\frac{AB}{AX}$$=\frac{AX+XB}{AX}$

$=1+\frac{XB}{AX}$

$=1+\frac{ZB}{CZ}$

$=\frac{CZ+ZB}{CZ}=\frac{BC}{CZ}$

$\therefore$ $\frac{AX}{AB}=\frac{CZ}{BC}$