4MA0 Foundation January 2015 Paper 2 Q23
23
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