4400 Higher June 2007 Paper 3 Q11
11
Diagram NOT accurately drawn
\(A\) and \(B\) are points on a circle, centre \(O\).
The lines \(CA\) and \(CB\) are tangents to the circle.
\(CA = 5.7\) cm.
\(CO = 6.9\) cm.
(a) Give a reason why angle \(CAO = 90^\circ\). (1)
(b) Calculate the perimeter of the kite \(CAOB\).
Give your answer correct to 3 significant figures. (5)
Give your answer correct to 3 significant figures. (5)
| Scheme | Marks |
|---|---|
| tangent at any point of a circle and the radius at that point are perpendicular | B1 |
| (1) |
Notes
B1: for mention of tangent and radius or line from centre
| Scheme | Marks |
|---|---|
| \(6.9^2 - 5.7^2\) or 47.61 − 32.49 or 15.12 | M1 |
| \(\sqrt{6.9^2 - 5.7^2}\) | M1 |
| 3.88844... | A1 |
| \(2 \times 5.7 + 2 \times \text{“}3.88844...\text{”}\) | M1 |
| 19.2 | A1 |
| (5) | |
| (6 marks) |
Notes
M1: for squaring and subtracting
M1: (dep) for square root
A1: for 3.89 or better
M1: for \(2 \times 5.7 + 2 \times \text{“}3.888...\text{”}\) only
A1: for 19.2 or answer which rounds to 19.2 (19.176888...)