4MA1/2H Jun 2018, Question 22: Chord Properties
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Using a circle with centre O and straight lines through it, given AF = 7 cm, FB = 4 cm, BC = 5 cm and FD = 2 cm, calculate x, the length CE, showing all steps.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Chords AB and the diameter through D cross at F: AF × FB = FD × (2r − FD)
- 27 × 4 = 2(2r − 2), so 28 = 4r − 4 and r = 8
- 3Secants from C: CB × CA = CE × (CE + 2r)
- 45 × 16 = x(x + 16), so x² + 16x − 80 = 0
- 5(x − 4)(x + 20) = 0, and x is a length, so x = 4
Answer4
Stuck on a step? Read the free lesson: Chord Properties
Practise more chord properties 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 chord properties
Also searched as: 4MA1 2H June 2018 · 4MA1/2H · 4ma1 jun18 2h · question 22.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.