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0580/13 May/Jun 2023, Question 20: Angle in a Semicircle

Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Calculator · 3 marks

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The question, in short

Circle with centre O and diameter AB; C lies on the circumference with chords AC and BC. Angle CAB is 32° and angle ABC is x°. Name line AC and find x with a reason.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

State the mathematical name for the line AC in the circle diagram.

  1. 1AC joins two points on the circumference
  2. 2AC is a chord

AnswerChord

Part (b) · 2 marks

Calculate x, the size of angle ABC, and give a geometrical reason for the value.

  1. 1Angle ACB = 90° (angle in a semicircle)
  2. 2x = 180 − 90 − 32 = 58
  3. 3x = 58, because the angle in a semicircle = 90°

Answer58, angle in a semicircle = 90°

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Also searched as: 0580/13/M/J/23 · 0580_s23_qp_13 · 0580 s23 13 · question 20.
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