This study notes covers Worked Example 3 within Properties of Circles for GCSE Mathematics. Revise Properties of Circles in Geometry & Measures for GCSE Mathematics with 10 exam-style questions and 4 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 5 of 5 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 5
Practice
10 questions
Recall
4 flashcards
Worked Example 3
A chord AB is 16 cm long. The perpendicular distance from the centre O to the chord is 6 cm. Find the radius of the circle.
Solution
The perpendicular from the centre to a chord bisects the chord
So the perpendicular meets AB at its midpoint M
AM = MB = 16 ÷ 2 = 8 cm
We now have a right-angled triangle OMA:
- OM = 6 cm (given perpendicular distance)
- AM = 8 cm (half the chord)
- OA = radius (the hypotenuse)
Using Pythagoras: r² = 6² + 8²
r² = 36 + 64 = 100
r = √100 = 10 cm