10 Fig. 10 shows a sketch of the points \(\mathrm { A } ( 2,7 ) , \mathrm { B } ( 0,3 )\) and \(\mathrm { C } ( 8 , - 1 )\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2ebf7ad2-638f-4378-b98d-aadd0de4c766-4_579_748_301_657}
\captionsetup{labelformat=empty}
\caption{Fig. 10}
\end{figure}
- Prove that angle ABC is \(90 ^ { \circ }\).
- Find the equation of the circle which has AC as a diameter.
- Find the equation of the tangent to this circle at A . Give your answer in the form \(a y = b x + c\), where \(a , b\) and \(c\) are integers.