12 Fig. 12 shows the circle \(( x - 1 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25\), the line \(4 y = 3 x - 32\) and the tangent to the circle at the point \(\mathrm { A } ( 5,2 )\). D is the point of intersection of the line \(4 y = 3 x - 32\) and the tangent at A .
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{904025c9-6d68-4344-bd41-8c0fccfcf92f-07_750_773_1311_632}
\captionsetup{labelformat=empty}
\caption{Fig. 12}
\end{figure}
- Write down the coordinates of C , the centre of the circle.
- (A) Show that the line \(4 y = 3 x - 32\) is a tangent to the circle.
(B) Find the coordinates of B , the point where the line \(4 y = 3 x - 32\) touches the circle. - Prove that ADBC is a square.
- The point E is the lowest point on the circle. Find the area of the sector ECB .