4MA1/1HR Jun 2019, Question 23: Combining Circle Theorems
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Using a circle through B, C, D, F with straight lines ABC, AFD, BFE, CDE, angle A = 54° and angle E = 32°, work out angle x = angle CBE, showing working.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1BCDF is cyclic, so angle CDF = 180° − x and angle FDE = x
- 2Triangle DEF: angle DFE = 180° − 32° − x = 148° − x
- 3Angle AFB = angle DFE = 148° − x (vertically opposite)
- 4Triangle ABF: 54 + (180 − x) + (148 − x) = 180
- 5382 − 2x = 180, so x = 101
Answer101
Stuck on a step? Read the free lesson: Combining Circle Theorems
Practise more combining circle theorems questions
Real 4MA1 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: 4MA1 1HR June 2019 · 4MA1/1HR · 4ma1 jun19 1hr · question 23.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.