4400 Higher June 2004 Paper 3 Q18
18
Diagram NOT accurately drawn
\(A\), \(B\), \(C\) and \(D\) are four points on the circumference of a circle.
The chords \(AC\) and \(BD\) intersect at \(E\).
\(AE = 3.6\) cm, \(CE = 2.8\) cm, \(DE = 2.4\) cm and \(AD = 4.9\) cm.
(a) Calculate the length of \(BE\). (3)
(b) Calculate the size of angle \(AED\).
Give your answer correct to 3 significant figures. (3)
Give your answer correct to 3 significant figures. (3)
| Scheme | Marks |
|---|---|
| \(3.6 \times 2.8 = 2.4 \times BE\) | M1 |
| \(\dfrac{3.6 \times 2.8}{2.4}\) | M1 |
| 4.2 | A1 |
| (3) |
Notes
M1: Accept \(AE \times CE = BE \times ED\)
A1: cao
| Scheme | Marks |
|---|---|
| \(\dfrac{3.6^2 + 2.4^2 - 4.9^2}{2 \times 3.6 \times 2.4}\) | M1 |
| \(-0.3061\) | A1 |
| 108 | A1 |
| (3) | |
| (6 marks) |
Notes
A1: at least 3 sf
A1: for 108 or better (107.826…)