Question

In fig., if PQ $\parallel$ BC and PR $\parallel$CD, then, $\frac{AR}{AD}$=

• A. $\frac{AP}{AC}$
• B. $\frac{AC}{AP}$
• C. $\frac{AQ}{AB}$
• D. None of the above

Answer 1

The correct option is A $\frac{AP}{AC}$

In $\Delta ACD$, we have

$PR\parallel CD$ [Given]

Therefore, by basic proportionality theorem, we have

$\frac{AP}{PC}$ = $\frac{AR}{RD}$

$\Rightarrow \frac{PC}{AP}=\frac{RD}{AR}$

Adding 1 on both sides we get,

$\frac{PC+AP}{AP}=\frac{RD+AR}{AR}$

$\Rightarrow \frac{AC}{AP}=\frac{AD}{AR}$

$\Rightarrow \frac{AP}{AC}$ = $\frac{AR}{AD}$