Edexcel C2 2012 June — Question 3

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2012
SessionJune
TopicCircles

3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f1ef99f0-4ad4-49d8-bee7-d5bb9cc84660-04_734_1262_237_315} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} The circle \(C\) with centre \(T\) and radius \(r\) has equation $$x ^ { 2 } + y ^ { 2 } - 20 x - 16 y + 139 = 0$$
  1. Find the coordinates of the centre of \(C\).
  2. Show that \(r = 5\) The line \(L\) has equation \(x = 13\) and crosses \(C\) at the points \(P\) and \(Q\) as shown in Figure 1.
  3. Find the \(y\) coordinate of \(P\) and the \(y\) coordinate of \(Q\). Given that, to 3 decimal places, the angle \(P T Q\) is 1.855 radians,
  4. find the perimeter of the sector \(P T Q\).