Lemmara logoLemmaraWorked solution

0580/33 Oct/Nov 2022, Question 6: Combining Circle Theorems

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 9 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Use parallel lines ABC and ED with angles 48° and 57° to find p and q with reasons, then use a circle with tangent FHJ at G and OH = HJ to name triangle OHJ and find x and y.

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

Part (ai) · 2 marks

Find p using the parallel lines ABC and ED, giving a geometrical reason.

  1. 1p = 48
  2. 2Alternate angles (ABC is parallel to ED)

Answer48, alternate angles

Part (aii) · 2 marks

Find q using the parallel lines ABC and ED, giving a geometrical reason.

  1. 1q = 180 − 57 = 123
  2. 2Co-interior (interior) angles add to 180°

Answer123, interior angles

Part (bi) · 1 mark

State the mathematical name of triangle OHJ, given OH = HJ.

  1. 1OH = HJ: isosceles triangle

AnswerIsosceles

Part (bii) · 1 mark

Find x, the angle OJH, using the tangent and isosceles triangle facts.

  1. 1Base angles of isosceles triangle OHJ are equal: x = 28

Answer28

Part (biii) · 3 marks

Find y, angle HOG, using the tangent at G and angle JOH = 28°.

  1. 1Angle OGJ = 90° (tangent meets radius at 90°)
  2. 2In triangle OGJ: y + 28 + 90 + 28 = 180
  3. 3y = 180 − 90 − 28 − 28 = 34

Answer34

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 Lemmara

More past-paper questions on combining circle theorems

Also searched as: 0580/33/O/N/22 · 0580_w22_qp_33 · 0580 w22 33 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.