Lemmara logoLemmaraWorked solution

0580/33 May/Jun 2026, Question 25: Pythagoras' Theorem

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 5 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Circle with centre O and diameter AC; B lies on the circumference, AB = 14 cm and BC = 8 cm. Find the reason for angle ABC = 90°, then AC and angle BAC.

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

Part (a) · 1 mark

State the geometrical reason that angle ABC equals 90°.

  1. 1AC is a diameter, so angle ABC is the angle in a semicircle, which is 90°

AnswerAngle in a semicircle = 90°

Part (b) · 2 marks

Calculate the length AC using the given sides.

  1. 1AC² = 14² + 8²
  2. 2= 196 + 64 = 260
  3. 3AC = √260 = 16.12… ≈ 16.1 cm

Answer16.1 or 16.12…

Part (c) · 2 marks

Calculate the size of angle BAC.

  1. 1tan BAC = opposite/adjacent = 8/14
  2. 2BAC = tan⁻¹(8/14)
  3. 3= 29.74… ≈ 29.7°

Answer29.7 or 29.74…

Stuck on a step? Read the free lesson: Pythagoras' Theorem

Practise more pythagoras' theorem questions

Real 0580 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 pythagoras' theorem

Also searched as: 0580/33/M/J/26 · 0580_s26_qp_33 · 0580 s26 33 · question 25.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.