Lemmara logoLemmaraWorked solution

4024/22 Oct/Nov 2024, Question 9: Combining Circle Theorems

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 10 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Use circle geometry with a tangent and given angle to find a radius, then use an arc length to work out a major sector area.

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

Part (a) · 5 marks

With angle ABC 126° and tangent DE 10.5 cm, work out the circle's radius.

  1. 1Angle ADC = 180 − 126 = 54° (opposite angles of a cyclic quadrilateral)
  2. 2OC = OD, so angle OCD = 54° and angle DOC = 180 − 54 − 54 = 72°
  3. 3Angle ODE = 90° (tangent perpendicular to radius)
  4. 4tan 72 = 10.5/r, so r = 10.5 ÷ tan 72
  5. 5= 3.411… ≈ 3.41 cm

Answer3.41 or 3.411 to 3.412

Part (b) · 5 marks

Given minor sector angle 82° and minor arc 7.3 cm, find the major sector's area.

  1. 182/360 × 2πr = 7.3
  2. 2r = 7.3 × 360 ÷ (2π × 82) = 5.100… cm
  3. 3Major sector angle = 360 − 82 = 278°
  4. 4Area = 278/360 × π × 5.100…²
  5. 5= 63.11… ≈ 63.1 cm²

Answer63.1 or 63.10 to 63.13

Stuck on a step? Read the free lesson: Combining Circle Theorems

Practise more combining circle theorems questions

Real 4024 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on combining circle theorems

Also searched as: 4024/22/O/N/24 · 4024_w24_qp_22 · 4024 w24 22 · question 9.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.