Higher November 2023 Paper 3 Q21
21
\(A\), \(B\), \(C\) and \(D\) are points on the circumference of a circle, centre \(O\).
\(AC\) is a diameter of the circle.
\(ADE\) and \(BCE\) are straight lines.
Work out the size of angle \(BDC\).
Write down any circle theorems that you use. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 27 | M1 | for start by finding one missing angle, eg angle \(CBD = 35\) or angle \(ADC = 90\) or angle \(ACE = 117\) |
| M1 | for making progress by finding a second angle, eg angle \(BDE = 117\) or angle \(DCE = 62\) or angle \(BCA = 63\) | |
| A1 | for angle \(BDC = 27\) | |
| C1 | (dep on M1) for stating one correct circle theorem used eg Angles in a semicircle are 90 or Angles in the same segment are equal or Angles at the circumference subtended from the same arc of a circle are equal or The angle at the centre of a circle is twice the angle at the circumference |
Additional guidance
Angles clearly identified on the diagram or in the working space may be awarded marks provided there is no ambiguity or contradiction.
Underlined words need to be shown; circle theorems stated need to be linked to their method, which can be implied from correctly identified angles (stated or written on the diagram).