Question

In the given figure, $PQ>PR$ and $QS,RS$ are the bisectors of $\angle Q$ and $\angle R$ respectively, then __________.

• A. $SQ>SR$
• B. $SQ=SR$
• C. $SQ<SR$
• D. $SQ=\frac{1}{2}SR$

Answer 1

The correct option is A $SQ>SR$

Given that $PQ>PR$

Thus, $\angle Q<\angle R\Rightarrow \angle \frac{Q}{2}<\angle \frac{R}{2}$ (Bisected angles of angle Q and angle R)

$QS$ and $RS$ are the bisectors of $\angle Q$ and $\angle R$ respectively.

$\therefore \angle SQR<\angle SRQ$

Thus, $SQ>SR$