Higher November 2024 Paper 1 Q17
17 \(A\), \(B\) and \(C\) are points on a circle, centre \(O\).
\(CD\) is a tangent to the circle.
Angle \(BCD = 40^\circ\)
Angle \(OAB = 3 \times\) angle \(OAC\)
Work out the size of angle \(ACD\).
Write down any circle theorems that you use. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 100 | M1 | for angle \(BAC = 40\) |
| M1 | for angle \(OAC\) or angle \(OCA = 10\) or angle \(OAB\) or angle \(OBA = 30\) | |
| M1 | for angle \(ACB = (180 - 30 - 30) \div 2\ (= 60)\) or angle \(OCD = 90\) or angle \(OCB = 50\) | |
| C1 | for angle \(ACD = 100\) and one correct appropriate circle theorem from alternate segment theorem angle at the centre is twice the angle at the circumference the tangent to a circle is perpendicular to the radius |
Additional guidance
angle \(AOB = 120\) gets M1M1
Award M3C0 for answer of 100 with no correct appropriate circle theorem
Underlined words need to be shown
Reason needs to be linked to their method, which can be implied from correctly identified angles (stated or written on the diagram)