Question

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

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

Answer 1

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

In $\Delta ABC$, we have

$QP\parallel BC$ [Given]

Therefore, by basic proportionality theorem, we have

$\frac{AQ}{QB}$ = $\frac{AP}{PC}$

$\Rightarrow \frac{QB}{AQ}=\frac{PC}{AP}$

Adding 1 on both sides we get,

$\frac{QB+AQ}{AQ}=\frac{PC+AP}{AP}$

$\Rightarrow \frac{AB}{AQ}=\frac{AC}{AP}$