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0580/12 Oct/Nov 2023, Question 17: Circumference and Area of a Circle

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Calculator · 4 marks

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The question, in short

Circle with centre O and diameter AB, point C on the circle. Draw a tangent at A, find the radius from circumference 22.3 cm, and justify why angle BCA is 90°.

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

Part (a) · 1 mark

Draw a tangent line touching the circle at point A.

  1. 1Draw a ruled line through A perpendicular to the diameter AB (radius OA)

AnswerRuled tangent drawn at A

Part (b) · 2 marks

Given circumference 22.3 cm, calculate the radius of the circle.

  1. 12πr = 22.3
  2. 2r = 22.3 ÷ 2π = 3.548… ≈ 3.55 cm

Answer3.55 or 3.548 to 3.549…

Part (c) · 1 mark

State a geometrical reason why angle BCA equals 90° when AB is a diameter.

  1. 1AB is a diameter, and the angle in a semicircle is 90°

AnswerAngle in a semicircle is 90°

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