(a) In Fig.-2, if a circle touches the side $QR$ of $\triangle PQR$ at $S$ and extended sides $P Q$ and $P R$ at $M$ and $N$, respectively, then $\;\text{ prove that }\;PM=\;\frac{1}{2}(PQ+QR+PR)$OR(b) In Fig. 3, a triangle $ABC$ is drawn to circumscribe a circle of radius 4 $\mathrm{cm}$ such that the segments $BD$ and $DC$ into which $BC$ is divided by the point of contact $D$ are of lengths $6\,\mathrm{cm}$ and $8\,\mathrm{cm}$ respectively. If the area of $\triangle ABC$ is $84\,\mathrm{cm}^2$, find the lengths of sides $AB$ and $AC$.