What Is a Segment of a Circle?

How this region differs from a sector

Circle segments appear whenever a chord cuts off a cap from the circle. Their geometry depends on the associated arc, the chord length, and the central angle behind that arc.

This page keeps the chord and curved boundary visible as a pair so the region is read correctly, especially by students who are used to the word segment meaning a straight finite line piece.

If you draw the two radii to the chord's endpoints, the sector contains the circle segment plus a triangle. That comparison explains why segment-area questions often subtract a triangle from a sector. The cap is defined by the chord and arc, not by the two radii.

• A circle segment is the region between a chord and its arc.
• The border of the region is made from one straight chord and one curved arc.
• If the chord becomes a diameter, the figure is no longer treated as a circle segment in the usual classroom definition; it becomes a semicircle.
• Segment area is different from sector area because the boundaries are different.

Where circle segments help

• Use circle segments when studying cap-shaped regions cut off by chords.
• Use them in advanced area problems where a sector and a triangle are combined or compared.
• Use the term when a circle diagram highlights a region that does not include the center.

Segment-region errors to catch

• Do not confuse a circle segment with a line segment; the same word is being used in a different geometric context.
• Do not call the region a sector if one side of the boundary is a chord rather than a radius.
• Do not forget that the relevant arc and chord must share the same endpoints.