What it does
A sector is a slice of a circle, like a slice of pizza: two radii and the arc between them. A segment is the part between a chord and the arc. This page draws both and works out:
- the sector area (θ/360) × πr²,
- the arc length (θ/360) × 2πr and the sector’s perimeter,
- the segment area, sector minus the triangle made by the two radii,
- the major sector and segment (the rest of the circle).
A second picture shows the tangents from a point outside a circle: each tangent meets its radius at a right angle, the two tangents have the same length, and the angle between them and the angle between the radii add up to 180°.
It follows the Class 10 chapters circles (tangents) and areas related to circles (sectors and segments).
The triangle part of a segment uses ½ r² sin θ, which you can explore in trig ratio explorer. The tangent length comes from pythagoras proof playground. Draw your own tangent constructions in interactive geometry construction.
How to use it
- Drag the blue point on the circle, or use the θ slider, to set the angle at the centre (1° to 359°).
- Set the radius r in cm.
- Choose π = 22/7, 3.14 or exact π. Textbook answers usually use 22/7 (with radii that are multiples of 7) or 3.14.
- Choose whether to shade the sector or the segment.
- In the tangent picture, drag P around. The radius stands for 4 cm, so the lengths are easy to compare.
A worked example
The page starts with r = 21 cm, θ = 60° and π = 22/7.
- Sector area = (60/360) × 22/7 × 21² = 1/6 × 22/7 × 441 = 231 cm².
- Arc length = (60/360) × 2 × 22/7 × 21 = 22 cm; perimeter = 22 + 42 = 64 cm.
- The triangle has area ½ × 21² × sin 60° ≈ 190.96 cm², so the segment is about 231 − 190.96 = 40.04 cm².
For the tangents: with a radius of 4 cm and P 5 cm from the centre, PT = √(25 − 16) = 3 cm on both sides.
Tips
- θ/360 is the fraction of the whole circle: 90° is a quarter, 120° a third.
- For angles over 180°, the triangle sits on the other side of the chord, so the segment is the sector plus the triangle. The page handles this with the sine of the angle.
Check yourself
Four fresh questions each time: a sector area, an arc length, a tangent length and an angle between radii. Type the answer, press Check, and open the worked answer if you need it. Nothing is saved.
FAQ
Why do answers differ slightly between 22/7 and 3.14? Both are approximations of π (3.14159…). 22/7 ≈ 3.1429 and 3.14 is a little smaller.
Is this from the NCERT book? It covers the same topics with fibub’s own pictures and examples. fibub is not part of NCERT.
Where the numbers come from
- Standard results: sector area (θ/360)πr², arc length (θ/360)2πr, segment = sector − triangle, the tangent is perpendicular to the radius and the two tangents from a point are equal. Written for fibub.
- Checked against hand-worked answers (r = 21 cm, 60°, π = 22/7: 231 cm² and 22 cm) and on 300 random tangent cases.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.