4MA0 Higher January 2015 Paper 4 Q11
11
Diagram NOT accurately drawn
R and T are points on a circle, centre O.
ROP is a straight line.
PT is a tangent to the circle.
Angle \(TPO = 46^\circ\)
(a) Explain why angle \(OTP = 90^\circ\) (1)
(b) Work out the size of angle \(y\). (3)
| Scheme | Marks |
|---|---|
| Angle between tangent and radius is \(90^\circ\) | B1 |
| (1) |
Notes
B1: Accept perpendicular or right angle for \(90^\circ\)
| Scheme | Marks |
|---|---|
| angle \(POT = 180 - 90 - 46\) (=44) or \(2y + 90 + 46 = 180\) | M1 |
| \((y =)\) “44” ÷ 2 or (180 – (180 – 44)) ÷ 2 or \((y =)\) (180 – 90 – 46) ÷ 2 | M1 |
| 22 | A1 |
| (3) | |
| (4 marks) |
Notes
M1: May be on diagram