G2.4 On the coordinate plane, a circle with centre $T(3,3)$ passes through the origin $O(0,0)$. If $A$ is a point on the circle such that $\angle A O T=45^{\circ}$ and the area of $\triangle A O T$ is $Q$ square units, find the value of $Q$.
$\begin{array}{l}O T=\sqrt{3^{2}+3^{2}}=3 \sqrt{2} \\ O T=A T=\text { radii } \\ \angle O A T=45^{\circ} \text { (side opp. eq. } \angle \text { s) } \\ \angle A T O=90^{\circ}(\angle \text { s sum of } \triangle \text { ) } \\ Q=\frac{1}{2} O T \cdot A T=\frac{1}{2} \cdot(3 \sqrt{2})^{2}=9\end{array}$