Intermediate November 2023 Unit 1 Q18
18. The points B, C, D and E lie on the circumference of a circle, with centre O.
AF is a tangent to the circle.
AO is a straight line.
Diagram not drawn to scale
(a) Explain how you know that AOB is a right-angled triangle. [1]
(b) Calculate the size of angle \(x\).
You must show all your working. [3]
You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
| Statement explaining that, ‘The tangent at any point on a circle is perpendicular (or equivalent) to the radius at that point’. | E1 | Accept unambiguous similar wording. e.g. ‘Radius and tangent 90(°)’ ‘The angle between a tangent and radius is 90(°)’ Diameter could be used in place of radius. Must refer to tangent and radius by name (not simply AF and OB or description). |
| Scheme | Marks | Comments |
|---|---|---|
| (AOB =) 180 – 90 – 42 or 90 – 42 | M1 | Check diagram for answers. Note: 180 – 132 |
| 48 (°) | A1 | May be implied by sight of a final answer of 24. |
| \(x\) = 24(°) | B1 | FT ‘their 48’ ÷ 2, provided ‘their 48’ ≠ 42. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| 18.(b) Alternative method | Check diagram for answers. | |
| (\(x\) = ) \(\dfrac{180 - 90 - 42}{2}\) or \(\dfrac{90 - 42}{2}\) | M2 | Award M2 for complete method. |
| \(x\) = 24(°) | A1 |