Lemmara logoLemmaraWorked solution

0606/21 May/Jun 2026, Question 8: Using Trigonometry and Pythagoras Together

Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 8 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Circle centre C radius 10, A and B on circle, CBP straight with BP = x, AP tangent at A, angle ACB = θ, triangle APC perimeter 38. Find θ, arc AB and sector ACB area.

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

Part (a) · 6 marks

Use the tangent and right angle at A with perimeter 38 to show θ = 0.885 radians to 3 decimal places.

  1. 1Angle CAP = 90° (tangent ⊥ radius), CP = 10 + x
  2. 2AP = √((10 + x)² − 10²) = √(20x + x²), or from the perimeter AP = 18 − x
  3. 310² + (18 − x)² = (10 + x)²
  4. 4100 + 324 − 36x + x² = 100 + 20x + x², so 56x = 324, x = 81/14 = 5.7857…
  5. 5cos θ = 10/(10 + x) = 140/221
  6. 6θ = 0.8847… = 0.885

Answerθ = 0.8847… = 0.885 shown

Part (b) · 1 mark

Calculate the length of arc AB using radius 10 and angle θ.

  1. 1Arc AB = rθ
  2. 2= 10 × 0.88474… = 8.85

Answer8.85 (8.847…)

Part (c) · 1 mark

Calculate the area of sector ACB using radius 10 and angle θ.

  1. 1Sector area = (1/2)r²θ
  2. 2= (1/2)(100)(0.88474…) = 44.2

Answer44.2 or 44.3 (44.237…)

Stuck on a step? Read the free lesson: Using Trigonometry and Pythagoras Together

Practise more using trigonometry and pythagoras together questions

Real 0606 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 using trigonometry and pythagoras together

Also searched as: 0606/21/M/J/26 · 0606_s26_qp_21 · 0606 s26 21 · question 8.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.