2 Fig. 10 shows a sketch of a circle with centre \(\mathrm { C } ( 4,2 )\). The circle intersects the \(x\)-axis at \(\mathrm { A } ( 1,0 )\) and at B .
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{55e2d4f5-c84d-4577-988e-96071a220d60-2_689_811_430_662}
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\caption{Fig. 10}
\end{figure}
- Write down the coordinates of B .
- Find the radius of the circle and hence write down the equation of the circle.
- AD is a diameter of the circle. Find the coordinates of D .
- Find the equation of the tangent to the circle at D . Give your answer in the form \(y = a x + b\).