Question

If $E$ is a point on side $QR$ of $\Delta PQR$ such that $PE$ bisects $\angle QPR$, then :

• A. $QE=ER$
• B. $QP>QE$
• C. $QE>QP$
• D. $ER>RP$

Answer 1

Answer: (B)

$QP>QE$

According to the given condition $\angle QPE=\angle RPE$

And from external angle theorem,

$\angle PEQ=\angle RPE+\angle PRE$

$\Rightarrow \angle PEQ=\angle QPE+\angle PRE$

$\Rightarrow \angle PEQ>\angle QPE$

In triangle, side opposite angle is greater

$\Rightarrow QP>QE$