| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2019 |
| Marks | 7 |
| Topic | Circles |
| Type | Tangent equation at a known point on circle |
| Difficulty | Standard +0.3 This is a straightforward coordinate geometry question requiring standard techniques: finding the circle center (midpoint of diameter), finding the perpendicular tangent line, solving for x-intercept, and calculating triangle area. All steps are routine applications of formulas with no novel insight required, making it slightly easier than average. |
| Spec | 1.03b 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 |
\includegraphics{figure_7}
The diagram shows a circle which passes through the points $A(2, 9)$ and $B(10, 3)$. $AB$ is a diameter of the circle.
\begin{enumerate}[label=(\alph*)]
\item The tangent to the circle at the point $B$ cuts the $x$-axis at $C$. Find the exact coordinates of $C$. [4]
\item Find the exact area of the triangle formed by $B$, $C$ and the centre of the circle [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2019 Q7 [7]}}