One straight cut

The idea

A segment is the part of a circular region enclosed between a chord and the corresponding arc; a chord forms a minor and a major segment, and 'sector' or 'segment' alone means the minor one.

Cutting a round cheese

A round cheese is cut by one straight cut AB. The cut does not go through the centre O. The cheese falls into two pieces.

Which piece holds the centre O?

• The bigger piece
• The smaller piece
• Neither: O is on the cut

Tap the right piece

Each circle has a chord AB. Tap the piece you are asked for. Then press the button to see the next chord.

Two segments

A segment is the part of a circle between a chord and an arc. A chord AB makes a minor segment, the smaller piece, and a major segment, the bigger piece, which holds the centre O.

A sector has a corner at the centre O. A segment has no corner at O: it is closed by the chord on one side and the arc on the other.

When the book writes just "segment" or "sector", it means the minor one, unless it says otherwise.

Notes

A chord cuts a circle into a minor segment (smaller, without O) and a major segment (bigger, with the centre O).

Check yourself

A chord AB of a circle does not pass through the centre O. Which piece is the major segment?

In a circle, the region between the chord PQ and the arc PQ that does not contain the centre is called

A question asks for "the area of the segment" and says nothing more. Which segment is meant?

Which of these pieces of a circle has a corner at the centre O?

• The piece that holds the centre O — correct. Yes! The centre is always inside the bigger piece, so that piece is the major segment.
• The piece that does not hold the centre O. That is the smaller piece, the minor segment.
• The piece with the shorter arc. The shorter arc belongs to the smaller piece, the minor segment.
• the minor segment — correct. Yes! It is the smaller piece, the one without the centre.
• the major segment. The major segment is the piece that contains the centre.
• the minor sector. A sector is bounded by two radii. Here the piece is bounded by a chord and an arc, so it is a segment.
• The minor segment — correct. Yes! The book says "segment" means the minor segment unless stated otherwise.
• The major segment. Only if the question says "major". Without a word, it means the minor one.
• Both segments added. The two segments together are the whole circle. "The segment" means one piece, the minor one.
• A sector — correct. Yes! A sector is bounded by two radii, which meet at O.
• A segment. A segment is bounded by a chord and an arc. It has no corner at O.
• Both of them. Only a sector has two radii meeting at O. A segment has none.