| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2013 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Tangent from external point - find equation |
| Difficulty | Standard +0.3 This is a straightforward C2 circle question requiring basic geometric understanding. Part (a) is trivial (writing down the circle equation given center and radius). Part (b) uses the standard right-angle property of tangents with Pythagoras' theorem - a routine application requiring no novel insight, making it slightly easier than average. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle1.03f Circle properties: angles, chords, tangents |
10.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{1c51b071-5cb1-4841-b031-80bde9027433-16_723_979_207_495}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}
The circle $C$ has radius 5 and touches the $y$-axis at the point $( 0,9 )$, as shown in Figure 4.
\begin{enumerate}[label=(\alph*)]
\item Write down an equation for the circle $C$, that is shown in Figure 4.
A line through the point $P ( 8 , - 7 )$ is a tangent to the circle $C$ at the point $T$.
\item Find the length of $P T$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2013 Q10 [6]}}