Intermediate November 2018 Unit 1 Q16
16. A, B and C are points on the circumference of a circle with centre O.
\(A\hat{C}B\) = 74°.
Diagram not drawn to scale
Calculate the value of \(x\).
You must state any angle property of a circle that you use.
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| AOB = 148(°) | B1 | May be seen on the diagram. Do not accept 148 unless unambiguously associated with angle AOB (stated, or on diagram, or used for M1) |
| Angle subtended by an arc at the centre of a circle is twice the angle subtended at the circumference. | E1 | Dependent on 2 × 74 (= 148) seen. Accept any unambiguous wording. E0 for simply stating ‘twice 74’. |
| x = \(\dfrac{180 - 148}{2}\) | M1 | FT ‘their derived or stated angle AOB’. NOT 74°. x = 90 – 74 is B1E0M1 (E1 if a full and accurate explanation is given.) |
| = 16 | A1 | Unsupported (x =) 16 gains B1E0M1A1. |