Lemmara logoLemmaraWorked solution

4MA1/1H Jun 2018, Question 13: Angle at the Centre

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Circle with centre O through L, M, N; tangent QMT at M; angle NLM = 27°. Find angle NOM and angle NMQ, giving a reason for each.

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

Part (ai) · 1 mark

Find the size of angle NOM.

  1. 1angle at centre is twice angle at circumference
  2. 227 × 2 = 54

Answer54

Part (aii) · 1 mark

State the circle theorem that justifies the value of angle NOM.

  1. 1angle NOM is at the centre, angle NLM is at the circumference
  2. 2angle NOM = 2 × angle NLM

Answerangle at centre is twice angle at circumference

Part (bi) · 1 mark

Find the size of angle NMQ between chord NM and tangent QMT.

  1. 1angle between tangent and radius is 90°
  2. 2angle NMQ = 90° − angle OMN
  3. 3angle OMN = (180° − 54°) / 2 = 63°
  4. 4angle NMQ = 90° − 63° = 27°

Answer27

Part (bii) · 1 mark

State the reason justifying the value of angle NMQ.

  1. 1angle between tangent QMT and chord MN equals angle in alternate segment
  2. 2angle NMQ = angle MLN = 27°

Answeralternate segment theorem

Stuck on a step? Read the free lesson: Angle at the Centre

Practise more angle at the centre questions

Real 4MA1 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 angle at the centre

Also searched as: 4MA1 1H June 2018 · 4MA1/1H · 4ma1 jun18 1h · question 13.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.