Higher June 2023 Paper 1 Q21
21 \(A\), \(B\) and \(D\) are points on a circle with centre \(O\).
\(CDE\) is the tangent to the circle at \(D\).
Work out the size of angle \(ADC\).
Write down any circle theorems you use. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 71 | M1 | for method to find angle \(BAD\) or angle \(OAB\) or angle \(OBD\), eg angle \(BAD = 64 \div 2\ (= 32)\) or angle \(OAB = 51\) or angle \(OBD = (180 - 64) \div 2\ (= 58)\) |
| M1 | for method to find angle \(ADO\) or angle \(AXD\) (where \(X\) is a point on the major arc \(AD\)) eg \(ADO = 180 - 64 - (180 - 51 - \text{``}32\text{''})\ (= 19)\) or \(ADO = (180 - 64 - (180 - 2 \times \text{``}51\text{''})) \div 2\ (= 19)\) or angle \(AXD = 180 - \text{``}58\text{''} - 51\ (= 71)\) | |
| A1 | for angle \(ADC = 71\) | |
| C1 | (dep on M1) for one circle theorem relevant to their method, eg The angle at the centre of a circle is twice the angle at the circumference or The tangent to a circle is perpendicular to the radius (diameter) or Opposite angles of a cyclic quadrilateral add up to 180 or Alternate segment theorem |
Additional guidance
Angles may be seen on the diagram
Underlined words need to be shown; reasons need to be linked to their method