Question

In the figure, 2 AD = AB, P is the mid point of AB, Q is mid point of DR and $PR\parallel BS$. Then, $\frac{DS}{RS}=$

• A. AB = AP
• B. AB < AP
• C. AB > AP
• D. AB AP

Answer 1

The correct option is D

AB AP

Given: i) Q and A are mid points of RD and PD respectively.

(ii) $PR\parallel BS$.

Since A is mid point and Q is mid point, $AQ\parallel PR$ [mid-point theorem]

Also, $PR\parallel BS$, using equal intercept theorem, in $\Delta DBS$,

$\frac{DP}{PB}=\frac{DR}{RS}$

$\Rightarrow \frac{DP}{PB}+1=\frac{DR}{RS}+1$

$\Rightarrow \frac{DB}{PB}=\frac{DS}{RS}$

We know that $\frac{DB}{PB}=3$ because DA = AP = PB

So, $\frac{DS}{RS}=3$