0580/22 Oct/Nov 2023, Question 17: Combining Circle Theorems
Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Use circle theorems with a centre O and given angles to find two unknown angles in separate circle diagrams.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
Given angle OBA = 28° with A, B, C on a circle centre O, find angle ACB.
- 1OA = OB, so angle OAB = 28°
- 2Angle AOB = 180 − 28 − 28 = 124°
- 3Angle ACB = 124 ÷ 2 = 62° (angle at centre is twice angle at circumference)
Answer62
Part (b) · 2 marks
With tangent TU at P and angles TPR = 47°, PRQ = 52°, find angle RPQ.
- 1Angle RQP = 47° (alternate segment theorem)
- 2Angle RPQ = 180 − 52 − 47 = 81°
Answer81
Stuck on a step? Read the free lesson: Combining Circle Theorems
Practise more combining circle theorems questions
Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on combining circle theorems
Also searched as: 0580/22/O/N/23 · 0580_w23_qp_22 · 0580 w23 22 · question 17.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.