O-LevelMathematicsGeometry4024/11 · Oct/Nov 2022 · Q145 Marks
14 B, C and D are points on the circumference of a circle, centre O. AB is a tangent to the circle at B. BD is a diameter and OCA is a straight line. CÔDB = x°. Find an expression, in terms of x, for each of the following. Write each expression in its simplest form. [Figure of a circle with points B, C, D on circumference, O at centre, tangent AB, diameter BD, straight line OCA]
- (a)CÔB[1]
- (b)OÂB[2]
- (c)CBO[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [1] 2x
- [2] 90 - 2x or 2(45 – x) final answer
- B1 for ∠OBA = 90 soi or for answer correct but not in simplified form
- [2] 90 - x final answer
- B1 for ∠BCD = 90 soi or ∠CBA = x soi
- or M1 for (180 - their(a))/2 or 180 - (90+x)
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