4400 Higher November 2010 Paper 4 Q10
10
Diagram NOT accurately drawn
\(A\), \(B\) and \(C\) are points on a circle, centre \(O\).
\(AB\) is a diameter of the circle.
\(PC\) is a tangent to the circle.
\(ABP\) is a straight line.
Angle \(BAC = 21^\circ\).
Work out the size of angle \(APC\).
(4)
| Scheme | Marks |
|---|---|
| \(\angle ACO = 21^\circ\) or \(\angle COB = 42^\circ\) or \(\angle ACB = 90^\circ\) | B1 |
| \(\angle OCP = 90^\circ\) or \(\angle CBP = 111^\circ\) or \(\angle BCP = 21^\circ\) | B1 |
| 180 − 21 − (90 + 21) or 180 − 42 − 90 or 180 − 21 − 111 | M1 |
| 48 | A1 |
| (4) | |
| (4 marks) |
Notes
B1: Angles may be stated or marked on diagram
A1: Award 4 marks for an answer of 48, unless obtained by a clearly incorrect method.