Higher June 2017 Paper 3 Q18
18
\(A\), \(B\) and \(C\) are points on a circle of radius 5 cm, centre \(O\).
\(DA\) and \(DC\) are tangents to the circle.
\(DO = 9\) cm
Work out the length of arc \(ABC\).
Give your answer correct to 3 significant figures. (5)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| Note \(DOC = DOA\), \(ADO = CDO\) | 21.6 | P1 | Recognises that \(OAD\) or \(OCD\) is 90° or right angle |
| P1 | for using trigonometry to set up an equation in \(DOA\) or \(ADO\) eg \(\cos DOA = \dfrac{5}{9}\) | ||
| P1 | for using inverse trigonometry to find \(DOA\) or \(ADO\) eg \(DOA = \cos^{-1} \dfrac{5}{9}\ (= 56.25\ldots)\) | ||
| P1 | for a complete process to find arc length \(ABC\) or \(AC\) eg \(\dfrac{360 - 2 \times \text{``}56.25..\text{''}}{360} \times 2 \times \pi \times 5\ (= 21.598..)\) or \(\dfrac{2 \times \text{``}56.25..\text{''}}{360} \times 2 \times \pi \times 5\ (= 9.8174..)\) | ||
| A1 | for answer in the range 21.5 to 21.65 |