Higher January 2021 Paper 2R Q20
20 \(A\), \(B\) and \(C\) are points on a circle with centre \(O\).
Diagram NOT accurately drawn
Angle \(ABC = 75°\)
The area of the shaded segment is 200 cm2
Calculate the radius of the circle.
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| 75 × 2 (=150) | M1 |
| \(\dfrac{\text{“}150\text{”} \times \pi r^2}{360}\) oe \(\left(= 1.309r^2 \text{ or } \dfrac{5\pi}{12}r^2\right)\) | M1 |
| 0.5 × sin (“150”) × \(r^2\) oe (= 0.25\(r^2\)) | M1 |
eg \(\dfrac{150\pi}{360}r^2 - 0.5\sin(150)r^2 = 200\) oe or \((1.309\ldots - 0.25)r^2 = 200\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 13.7 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: “150” for AOC may be seen on diagram.
M1: dep 1st M1
M1: dep 1st M1
a complete method to find the area of triangle OAC in terms of r
M1: correct equation in \(r^2\) or rearranged to make \(r^2\) or \(r\) the subject.
A1: accept 13.7 – 13.8