4MA0 Higher January 2017 Paper 3R Q17
17 \(P\), \(R\), \(Q\) and \(S\) are four points on a circle.
Diagram NOT accurately drawn
\(RXS\) is a diameter of the circle.
\(PXQ\) is a chord of the circle.
\(PX = 4\) cm, \(\;XQ = 12\) cm, \(\;SX = 3\) cm.
Work out the radius of the circle.
(3)
| Scheme | Marks |
|---|---|
| e.g. \(\dfrac{12}{3} = \dfrac{RX}{4}\) or \(12 \times 4 = XR \times 3\) or \(3x = 48\) | M1 |
| (\(XR =\)) 12 × 4 ÷ 3 (=16) | M1 |
| 9.5 | A1oe |
| (3) | |
| (3 marks) |
Notes
M1: or \((2r - 3) \times 3 = 12 \times 4\)
M1: or \(2r - 3 = 12 \times 4 \div 3\) or \(XR = 16\) or an answer of 19
A1oe: e.g. \(\dfrac{19}{2}\)