4MA0 Higher January 2015 Paper 4R Q16
16
Diagram NOT accurately drawn
A, B, C and D are points on a circle.
AB is a diameter of the circle.
DC is parallel to AB.
Angle \(BAD = 70^\circ\)
(a) Calculate the size of angle BDC. (2)
The tangent to the circle at D meets the line BC extended at T.
(b) Calculate the size of angle BTD. (3)
| Scheme | Marks |
|---|---|
| \(\angle ADB = 90^\circ\) | M1 |
| 180 – 90 – 70 Answer: 20 | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| Position of T shown on diagram | M1 |
| \(\angle TDC\ (= \angle DBC) = 50^\circ\) | M1 |
| 180 – 70 – 50 or 180 – 50 – (180 – 110) Answer: 60 | A1 |
| (3) | |
| (5 marks) |