Higher January 2022 Paper 1R Q14
14
Diagram NOT accurately drawn
\(A\), \(B\), \(C\) and \(D\) are points on a circle, centre \(O\)
\(AOC\) is a diameter of the circle.
Angle \(BAC = 55^\circ\)
Work out the size of angle \(ADB\)
Give a reason for each stage of your working.
(4)
| Scheme | Marks |
|---|---|
| \(ABC = 90^\circ\) and \(ACB\ (= ADB) = 180 - 90 - 55\ (= 35)\) or \(ABO = 55^\circ\) and \(AOB = 180 - 2 \times 55\ (= 70)\) or \(BDC = 55^\circ\), \(ADC = 90^\circ\) and \(ADB = 90 - 55\ (= 35)\) | M1 |
| Working required Answer: 35 | A1 |
| Angles in a semicircle are 90° Angles in a triangle add to 180° (Angles in a triangle add to 180°) Angles in the same segment (are equal) OR angles at the circumference subtend(ed) from the same arc/chord of the circle (are equal) or Angles in an isosceles triangle (are equal) Angles in a triangle sum to 180° (Angles in a triangle add to 180°) Angle at the centre is 2 × (double) angle at circumference / angle at circumference is ½ angle at centre or Angles in the same segment (are equal) OR angles at the circumference subtend(ed) from the same arc/chord of the circle Angles in a semicircle are 90° | B2 |
| (4) | |
| (4 marks) |
Notes
A1: for \(ADB = 35\)
B2: (dep on M1) for all 3 reasons appropriate to their method
B1 (dep on M1) for one correct circle theorem appropriate to their method)
NB For the third method only 2 reasons are required