4400 Higher November 2004 Paper 3 Q7
7 The diagram shows a circle, centre \(O\).
\(PTQ\) is the tangent to the circle at \(T\).
\(PO = 6\) cm.
Angle \(OPT = 40^\circ\).
Diagram NOT accurately drawn
(a) Explain why angle \(OTP = 90^\circ\). (1)
(b) Calculate the length of \(OT\).
Give your answer correct to 3 significant figures. (3)
Give your answer correct to 3 significant figures. (3)
(c) Angle \(QOT = 36^\circ\).
Calculate the length of \(OQ\).
Give your answer correct to 3 significant figures. (3)
Calculate the length of \(OQ\).
Give your answer correct to 3 significant figures. (3)
| Scheme | Marks |
|---|---|
| Tangent, radius | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(\sin 40^\circ = \dfrac{OT}{6}\) | M1 |
| \(OT = 6\sin 40^\circ\) | M1 |
| 3.86 cm | A1 |
| (3) |
Notes
A1: or better
| Scheme | Marks |
|---|---|
| \(\cos 36^\circ = \dfrac{\text{his } 3.86}{OQ}\) | M1 |
| \(OQ = \dfrac{\text{his } 3.86}{\cos 36^\circ}\) | M1 |
| 4.77 or 4.8 cm | A1ft |
| (3) | |
| (7 marks) |
Notes
A1ft: or better