Question

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

• A. $\frac{RD}{QB}$
• B. $\frac{QB}{RD}$
• C. $\frac{AP}{PC}$
• D. $\frac{AC}{AP}$

Answer 1

The correct option is A $\frac{RD}{QB}$

In $\Delta ABC$, we have

$PQ\parallel CB$ [Given]

Therefore, by basic proportionality theorem, we have

$\frac{AQ}{QB}$ = $\frac{AP}{PC}........\left(1\right)$

In $\Delta ACD$, we have

$PR\parallel CD$ [Given]

Therefore, by basic proportionality theorem, we have

$\frac{AP}{PC}$ = $\frac{AR}{RD}........\left(2\right)$

From (1) and (2), we obtain that

$\frac{AQ}{QB}$ = $\frac{AR}{RD}$

$\Rightarrow \frac{AR}{AQ}$ = $\frac{RD}{QB}$