Higher June 2025 Paper 3 Q20
20 \(A\), \(B\), \(C\) and \(D\) are points on a circle with centre \(O\).
Find the size of angle \(OBC\).
Write down any circle theorems that you use. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 57 | M1 | for method to find angle \(BCD\) eg \(BCD = 180 - 80\ (= 100)\) |
| M1 | for method to find angle \(DOB\) eg \(DOB = 80 \times 2\ (= 160)\) | |
| A1 | for \(OBC = 57\) | |
| C1 | (dep on M1) for one correct circle theorem appropriate to their method eg The angle at the centre of a circle is twice the angle at the circumference or The angle at the circumference of a circle is half the angle at the centre or Opposite angles of a cyclic quadrilateral add up to 180 |
Additional guidance
Angles may be seen on diagram
Method marks can be awarded in either order
Correct method can be implied from angles on the diagram if no ambiguity or contradiction.
eg Angle \(O\) = 160 is too ambiguous
accept angle \(C\) = 100
Underlined words need to be shown; reasons need to be linked to their method.
Accept “\(\angle\)” for “angle” and “\(\angle s\)” for “angles”
Accept “4-sided shape” for “quadrilateral”