Mathematics
Mathematics
Problem
You are given a circle drawn on a sheet of paper, but its centre is not marked. a. (i) Describe, step by step, how you would locate the centre of the circle using only a ruler and a compass. b. (ii) Explain why the method you have described is always successful, referring to the properties of chords of a circle.Intuitive explanation
The key insight is that any chord's perpendicular bisector must pass through the center—so if you can construct two different perpendicular bisectors, their intersection reveals the center. You'll use a straightedge and compass to find perpendicular bisectors of chords, turning an unmarked circle into a fully locatable one.
Intuitive explanation
The key insight is that any chord's perpendicular bisector must pass through the center—so if you can construct two different perpendicular bisectors, their intersection reveals the center. You'll use a straightedge and compass to find perpendicular bisectors of chords, turning an unmarked circle into a fully locatable one.