Foundation June 2023 Paper 2 Q23
23
Diagram NOT accurately drawn
\(A\) and \(C\) are points on a circle, centre \(O\)
\(DA\) is the tangent to the circle at \(A\) and \(DC\) is the tangent to the circle at \(C\)
Angle \(ADC\) = 48°
Work out the size of reflex angle \(AOC\)
(3)
| Scheme | Marks |
|---|---|
| \(DCO\) = 90 (or right (angle)) or \(DAO\) = 90 (or right (angle)) Could also be awarded for \(CAO + CAD = 90\) or \(DAC + CAO = 90\) | M1 |
| Obtuse \(AOC = 360 - 90 - 90 - 48\) (= 132)oe or Obtuse \(AOC = 2(180 - (0.5 \times 48) - 90)\) (= 132) or Obtuse \(AOC = 180 - \text{``}{24}\text{''} - \text{``}{24}\text{''}\) or \(180 - 48\) (if working with \(\triangle DAC\) and \(\triangle OAC\)) or Reflex \(AOC = 90 + 90 + 48\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 228 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: may be marked on diagram – also allow right angle ’square’ symbol on diagram
M1: dep on M1 being awarded
may be marked on diagram
A1: SC if no other marks awarded 132 gains B1
M2 implied by \(360 - 90 - 90 - 48\) or \(360 - 228\)