4MA0 Higher June 2013 Paper 4 Q19
19 The sides of triangle \(PQR\) are tangents to a circle.
The tangents touch the circle at the points \(S\), \(T\) and \(U\).
\(QS = 6\) cm. \(PS = 7\) cm.
Diagram NOT accurately drawn
(a)
(i) Write down the length of \(QT\).
(ii) Give a reason for your answer.
(2)The perimeter of triangle \(PQR\) is 42 cm.
(b) Calculate the size of angle \(PQR\).
Give your answer correct to 1 decimal place. (4)
Give your answer correct to 1 decimal place. (4)
| Scheme | Marks |
|---|---|
| (i) 6 | B1 |
| (ii) Tangents from a point to a circle are equal in length | B1 |
| (2) |
Notes
B1: oe
| Scheme | Marks |
|---|---|
| \(RT\) (or \(RU\)) = 8 | B1 |
| \(\text{“}15\text{”}^2 = 13^2 + \text{“}14\text{”}^2 - 2 \times 13 \times \text{“}14\text{”} \cos(PQR)\) | M1 ft |
| \(\cos(PQR) = (13^2 + \text{“}14\text{”}^2 - \text{“}15\text{”}^2) \div (2 \times 13 \times \text{“}14\text{”})\) | M1 ft |
| 67.4 | A1 |
| (4) |
Notes
B1: or \(QR = 14\)
M1 ft: Allow ft for \(QR\) and \(PR\) if lengths stated or marked on diagram
A1: awrt 67.4