Circles
50. Circle Slices · Discover segments, minor & major parts
The chord always divides the circle into two segments.
A chord divides a circle into two regions, each called a segment. The smaller region is the minor segment; the larger is the major segment. Don't confuse a circle segment with a line segment — different meaning of the same word.
What this lesson covers
Try to break it
Drag points A and B around the circle. Watch how the chord moves and the two segments change size. The smaller piece is the minor segment, and the larger piece is the major segment.
How you build it
Draw a chord to make a segment.
- Draw a circle.
- Mark point A on the circle.
- Mark point B on the circle.
- Join A and B to draw the chord — it cuts the circle into two segments.
The proof, step by step
Prove that a chord divides the circle into two segments.
- A chord divides a circle into two segments.
- The smaller part is the minor segment; the larger part is the major segment.
- A diameter divides the circle into two equal semi-circles.
Worked example
A chord divides a circle into two segments. Which segment always contains the centre of the circle?
The major segment always contains the centre of the circle because it is the larger region enclosed by the chord and the major arc. The minor segment lies entirely on one side of the chord away from the centre.
- Minor segment
- Major segment — correct
- Semi-circle
- Neither segment