3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f1ef99f0-4ad4-49d8-bee7-d5bb9cc84660-04_734_1262_237_315}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The circle \(C\) with centre \(T\) and radius \(r\) has equation
$$x ^ { 2 } + y ^ { 2 } - 20 x - 16 y + 139 = 0$$
- Find the coordinates of the centre of \(C\).
- Show that \(r = 5\)
The line \(L\) has equation \(x = 13\) and crosses \(C\) at the points \(P\) and \(Q\) as shown in Figure 1.
- Find the \(y\) coordinate of \(P\) and the \(y\) coordinate of \(Q\).
Given that, to 3 decimal places, the angle \(P T Q\) is 1.855 radians,
- find the perimeter of the sector \(P T Q\).