15.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ea81408b-e292-4529-b1e2-e3246503a3ac-23_830_938_269_520}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Diagram not drawn to scale
The circle shown in Figure 4 has centre \(P ( 5,6 )\) and passes through the point \(A ( 12,7 )\).
Find
- the exact radius of the circle,
- an equation of the circle,
- an equation of the tangent to the circle at the point \(A\).
The circle also passes through the points \(B ( 0,1 )\) and \(C ( 4,13 )\).
- Use the cosine rule on triangle \(A B C\) to find the size of the angle \(B C A\), giving your answer in degrees to 3 significant figures.