Intermediate November 2016 Unit 2 Q17
17. Points A, B, C and D lie on the circumference of a circle, centre O.
BD is a diameter of the circle.
The straight line BC = 4·7 cm and \(B\widehat{A}C\) = 28°.
Diagram not drawn to scale
Write down the size of \(B\widehat{D}C\).
Hence, calculate the length BD. [5]
You must show all your working.
| Scheme | Marks | Comments |
|---|---|---|
| BDC = 28(°) | B1 | Angles may be shown on the diagram. Allow D = 28. |
| BCD = 90(°) | B1 | May be implied in later work. (Allow this B1 for any use of a right-angle triangle trigonometric relationship for triangle BCD) |
| BD = \(\dfrac{4{\cdot}7}{\text{Sin } 28}\) | M2 | This implies previous B mark. FT ‘their BDC’. M1 for \(\dfrac{4{\cdot}7}{\text{BD}}\) = sin 28. |
| BD = 10(·…)(cm) | A1 |
Alternative method
| COB = 56(°) | B1 |
| OB =\(\dfrac{2{\cdot}35}{\sin 28}\) (M1 for \(\dfrac{2{\cdot}35}{\text{OB}}\) =sin 28 ) | M2 |
| OB = 5(·…)(cm) | A1 |
| BD = 10(·..)(cm) | A1 |