| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Session | Specimen |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Chord length calculation |
| Difficulty | Standard +0.3 This is a multi-part circle geometry question requiring standard techniques: finding circle equation from center and point, tangent equation using perpendicular radius, and chord length using perpendicular distance from center. While it has multiple steps (3 parts), each uses routine C1/C2 methods with no novel insight required. The chord length calculation is slightly above average difficulty but still a textbook exercise. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.03b Straight lines: parallel and perpendicular relationships1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
12. The circle $C$ has centre $A ( 2,1 )$ and passes through the point $B ( 10,7 )$
\begin{enumerate}[label=(\alph*)]
\item Find an equation for $C$.
The line $l _ { 1 }$ is the tangent to $C$ at the point $B$.
\item Find an equation for $l _ { 1 }$
The line $l _ { 2 }$ is parallel to $l _ { 1 }$ and passes through the mid-point of $A B$.\\
Given that $l _ { 2 }$ intersects $C$ at the points $P$ and $Q$,
\item find the length of $P Q$, giving your answer in its simplest surd form.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 Q12 [11]}}