4MA0 Higher January 2016 Paper 3R Q10
10 The diagram shows a circle with centre \(O\).
The points \(A\), \(B\) and \(C\) lie on the circle.
Angle \(AOB = 96^\circ\)
Diagram NOT accurately drawn
(a) Work out the size of angle \(ACB\). (1)
\(AB = 16\) cm
(b) Work out the radius of the circle.
Give your answer correct to 3 significant figures. (4)
Give your answer correct to 3 significant figures. (4)
| Scheme | Marks |
|---|---|
| 48 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| angle \(AOM = 48^\circ\) and \(AM = 8\) (where \(M\) is the midpoint of \(AB\)) or angle \(OAB = 42^\circ\) (may be shown on diagram) | M1 |
| \(\sin 48 = \dfrac{8}{r}\) or \(\dfrac{16}{\sin 96} = \dfrac{r}{\sin 42}\) or \(16^2 = r^2 + r^2 - 2r^2 \cos 96\) oe | M1 |
| \(r = \dfrac{8}{\sin 48}\) or \(r = \dfrac{16 \sin 42}{\sin 96}\) or \(r = \sqrt{\dfrac{16^2}{2(1 - \cos 96)}}\) oe | M1 |
| 10.8 | A1 |
| (4) |
Notes
M1: For an expression involving \(r\) or \(r^2\)
Implies first M1
M1: For a correct expression for \(r\)
A1: awrt 10.8