| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Circles |
| Type | Perpendicular bisector of chord |
| Difficulty | Moderate -0.8 This is a straightforward C1 circle question requiring basic coordinate geometry: finding gradient, midpoint, perpendicular line equation, and distance formula. All steps are routine applications of standard formulas with no problem-solving insight needed, making it easier than average but not trivial due to the multi-step nature and arithmetic involved. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships1.03d Circles: equation (x-a)^2+(y-b)^2=r^2 |
\includegraphics{figure_1}
The points $A$ and $B$ have coordinates $(2, -3)$ and $(8, 5)$ respectively, and $AB$ is a chord of a circle with centre $C$, as shown in Fig. 1.
\begin{enumerate}[label=(\alph*)]
\item Find the gradient of $AB$. [2]
\end{enumerate}
The point $M$ is the mid-point of $AB$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find an equation for the line through $C$ and $M$. [5]
\end{enumerate}
Given that the $x$-coordinate of $C$ is 4,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the $y$-coordinate of $C$, [2]
\item show that the radius of the circle is $\frac{5\sqrt{17}}{4}$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q33 [13]}}