8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e3faf018-37a8-48ef-b100-81402a8ec87f-11_1262_1178_203_386}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of the circle \(C\) with centre \(N\) and equation
$$( x - 2 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = \frac { 169 } { 4 }$$
- Write down the coordinates of \(N\).
- Find the radius of \(C\).
The chord \(A B\) of \(C\) is parallel to the \(x\)-axis, lies below the \(x\)-axis and is of length 12 units as shown in Figure 3.
- Find the coordinates of \(A\) and the coordinates of \(B\).
- Show that angle \(A N B = 134.8 ^ { \circ }\), to the nearest 0.1 of a degree.
The tangents to \(C\) at the points \(A\) and \(B\) meet at the point \(P\).
- Find the length \(A P\), giving your answer to 3 significant figures.