| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Circles |
| Type | Circle from diameter endpoints |
| Difficulty | Standard +0.3 This is a multi-part question requiring standard techniques: gradient calculation for perpendicularity, triangle area formula, recognizing that a right angle subtends a diameter (Thales' theorem), finding circle equations from diameter endpoints, and maximizing distance. While it has multiple parts (4 marks worth), each step uses routine C1/C2 methods with no novel problem-solving required, making it slightly easier than average. |
| 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^21.03f Circle properties: angles, chords, tangents |
11 The points $A ( - 1,6 ) , B ( 1,0 )$ and $C ( 13,4 )$ are joined by straight lines.\\
(i) Prove that the lines AB and BC are perpendicular.\\
(ii) Find the area of triangle ABC .\\
(iii) A circle passes through the points A , B and C . Justify the statement that AC is a diameter of this circle. Find the equation of this circle.\\
(iv) Find the coordinates of the point on this circle that is furthest from B .
\hfill \mbox{\textit{OCR MEI C1 2011 Q11 [13]}}