G3.1 In Figure $1, P Q R S$ is a cyclic quadrilateral, where $S$ is on the straight line $R T$ and $T P$ is tangent to the circle. If $R S=8 \mathrm{~cm}$, $R T=11 \mathrm{~cm}$ and $T P=k \mathrm{~cm}$, find the value of $k$.
$\begin{array}{l}\text { Join } P R . \angle S P T=\angle P R S \text { ( } \angle \text { in alt. seg.) } \\ \angle S T P=\angle P T R \text { (common } \angle \text { ) } \\ \quad \triangle S T P \sim \triangle P T R \text { (equiangular) } \\ \left.\frac{T P}{T R}=\frac{T S}{T P} \quad \text { (ratio of sides, } \sim \Delta\right) \frac{k}{11}=\frac{11-8}{k} ; k=\sqrt{33}\end{array}$