Segment of a circle
- CBSE · NCERT Class 10, Ch 11 Areas Related to Circles
A segment is the part of a circle cut off between a chord and the arc it joins.
Draw a chord across a circle. It splits the circle into two segments, the minor segment and the major segment. To find a segment's area, start with the sector on the same arc. Then take away the triangle made by the two radii and the chord.
A small example
A circle has radius 14 cm, and a chord makes an angle of 90° at the centre. The sector's area is 1/4 × 22/7 × 14 × 14 = 154 cm². The triangle's area is 1/2 × 14 × 14 = 98 cm². So the minor segment is 154 − 98 = 56 cm².
Where marks go
Question 7 of CBSE's 2025-26 Maths Standard sample paper asks for the total area of eight equal segments where the Olympic rings overlap. The 2025-26 Maths Standard marking scheme works it as 8 × (one sector − one triangle). It is a 1-mark multiple-choice question. Every option includes the triangle part, so the sector alone matches none of them.
Show the sector area and the triangle area as separate lines. With step marking, each correct step can earn its own mark. If a question gives its own values for π or √3, use those instead of 22/7.
Sources
Facts last checked against these sources on 30 September 2026.
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