4MA0 Higher January 2013 Paper 4 Q22
22

Diagram NOT accurately drawn
\(A\), \(B\) and \(C\) are points on a circle, centre \(O\).
Angle \(ACB\) = 76°
\(PA\) and \(PB\) are tangents to the circle.
Calculate the size of angle \(APB\).
(4)
| Scheme | Marks |
|---|---|
| \(\angle PAO = 90°\) or \(\angle PBO = 90°\) | M1 |
| \(\angle AOB = 2 \times 76°\) or 152° or \(\angle POA = 76°\) or \(\angle POB = 76°\) | M1 |
| 360 − (“152” + 90 + 90) or 2 × (180 − 76 − 90) or 180 − 2×76 | M1 |
| 28 | A1 |
| (4) |
Notes
M1: or M2 for \(\angle PBA = 76°\) or \(\angle PAB = 76°\)
M1: implies previous two marks
Angles may be stated or marked on diagram or used in calculations provided any use is not ambiguous