Question

In the given figure, PQ>PR. QS and RS are the bisectors of $\angle Q$ and $\angle R$, respectively then which of the following is true?

• A. $SQ>SR$
• B. $\angle SRQ<\angle SQR$
• C. $SQ=SR$
• D. None of these

Answer 1

The correct option is A

$SQ>SR$

In $\Delta PQR$, we have
$PQ>PR$ (Given)
$\Rightarrow \angle PRQ>\angle PQR$ [Angle opp. to longer side of a triangle is greater]
$\Rightarrow \frac{1}{2}\angle PRQ>\frac{1}{2}\angle PQR$
$\Rightarrow \angle SRQ>\angle SQR$ [$\because RS$ is the bisector of $\angle PRQ$ and QS is the bisector of $\angle PQR$]
Now, in $\Delta SQR$.
$\angle SRQ>\angle SQR$ [Proved above]
Hence, $SQ>SR$. [$\because$ Side opposite to greater angle is longer].