| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Circle from diameter endpoints |
| Difficulty | Moderate -0.8 This is a straightforward multi-part circle question requiring standard techniques: midpoint formula for centre, distance formula for radius, expanding circle equation, and finding a tangent line using perpendicular gradients. All methods are routine C1 procedures with no problem-solving insight needed, making it easier than average but not trivial due to the computational steps involved. |
| 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 |
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The diagram shows a circle which passes through the points $A ( 2,9 )$ and $B ( 10,3 ) . A B$ is a diameter of the circle.\\
(i) Calculate the radius of the circle and the coordinates of the centre.\\
(ii) Show that the equation of the circle may be written in the form $x ^ { 2 } + y ^ { 2 } - 12 x - 12 y + 47 = 0$.\\
(iii) The tangent to the circle at the point $B$ cuts the $x$-axis at $C$. Find the coordinates of $C$.
\hfill \mbox{\textit{OCR C1 Q7 [13]}}