| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Circle through three points using right angle in semicircle |
| Difficulty | Moderate -0.8 This is a straightforward C1 circle question requiring only standard techniques: midpoint formula for the centre, distance formula for radius, and recall that angles in a semicircle are 90°. All parts are routine textbook exercises with no problem-solving or novel insight required, making it easier than average but not trivial due to the algebraic manipulation needed in part (ii). |
| 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 |
The points $P$ and $Q$ have coordinates $(-2, 6)$ and $(4, -1)$ respectively.
Given that $PQ$ is a diameter of circle $C$,
\begin{enumerate}[label=(\roman*)]
\item find the coordinates of the centre of $C$, [2]
\item show that $C$ has the equation
$$x^2 + y^2 - 2x - 5y - 14 = 0. \quad [5]$$
\end{enumerate}
The point $R$ has coordinates $(2, 7)$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Show that $R$ lies on $C$ and hence, state the size of $\angle PRQ$ in degrees. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 Q6 [9]}}