7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0aafa21b-25f4-4f36-b914-bbaf6cae7a66-19_739_871_260_532}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The circle with equation
$$x ^ { 2 } + y ^ { 2 } - 20 x - 16 y + 139 = 0$$
had centre \(C\) and radius \(r\).
- Find the coordinates of \(C\).
- Show that \(r = 5\)
The line with equation \(x = 13\) crosses the circle at the points \(P\) and \(Q\) as shown in Figure 1 .
- Find the \(y\) coordinate of \(P\) and the \(y\) coordinate of \(Q\).
A tangent to the circle from \(O\) touches the circle at point \(X\).
- Find, in surd form, the length \(O X\).
\includegraphics[max width=\textwidth, alt={}, center]{0aafa21b-25f4-4f36-b914-bbaf6cae7a66-22_2673_1948_107_118}