(a) In Fig.-2, if a circle touches the side QR of PQR at S and extended sides PQ and PR at M and N, respectively, then Fig. 2 prove that PM =1/2( PQ…

In Fig.-$\displaystyle 2$, if a circle touches the side QR of $\displaystyle \triangle \mathrm{PQR}$ at S and extended sides PQ and PR at M and N, respectively, then

Fig. $\displaystyle 2$ prove that $\displaystyle \mathrm{PM}=\frac{1}{2}(\mathrm{PQ}+\mathrm{QR}+\mathrm{PR})$

In Fig. $\displaystyle 3$, a triangle ABC is drawn to circumscribe a circle of radius $\displaystyle 4$ cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths $\displaystyle 6$ cm and $\displaystyle 8$ cm respectively. If the area of $\displaystyle \triangle \mathrm{ABC}$ is $\displaystyle 84 \mathrm{~cm}^{2}$, find the lengths of sides AB and AC . Fig. $\displaystyle 3$