Question

In $\Delta$PQR, seg RS is the bisector of $\angle$ PRQ, PS$=6$, SQ$=8$, PR$=24$. Find QR.

Answer 1

Using angle bisector theorem,

$\frac{PS}{SQ}=\frac{PR}{QR}$

$\Rightarrow \frac{6}{8}=\frac{24}{QR}$

$\Rightarrow QR=\frac{24\times 8}{6}=4\times 8=32$