(A) Two tangents $TP$ and $TQ$ are drawn to a circle with centre $O$ from an external point $T$ . Prove that $\angle PTQ = 2 \angle OPQ$ .OR(B) $A$ circle touches the side $BC$ of a $\triangle ABC$ at a point $P$ and touches $AB$ and $AC$ when produced at $Q$ and $R$ respectively. Show that $AQ = \;\frac{1}{2}$ (Perimeter of $\triangle ABC$ ).