Chapter 11 — Areas Related to Circles

Chapter 11 of the Class 10 Maths NCERT textbook, "Areas Related to Circles", teaches students to calculate the area and arc length of a sector using (θ/360) × πr², and the area of a segment by subtracting the corresponding triangle's area from the sector's area.

• Sectors and segments — A sector is the pie-slice region between two radii and their arc, while a segment is the region cut off between a chord and its arc. Each comes in a smaller minor form and a larger major form.
• The unitary method behind the formulas — Since the full 360° circle has area πr², a sector of angle θ takes just the θ/360 fraction of it. The same proportion gives the arc length, so every sector formula flows from this one idea.
• Finding a segment's area — A segment's area is what remains after removing the triangle formed by the two radii and the chord from its sector. Major areas are then found by subtracting the minor part from the whole circle.

1. 01A sector is the region enclosed by two radii and an arc; a segment is the region between a chord and its arc — both come in minor and major variants.
2. 02Area of a sector with radius r and central angle θ (in degrees) = (θ/360) × πr².
3. 03Length of an arc of a sector with radius r and angle θ = (θ/360) × 2πr.
4. 04Area of a segment = Area of the corresponding sector − Area of the corresponding triangle (formed by the two radii and the chord).
5. 05Area of the major sector = πr² − Area of the minor sector; area of the major segment = πr² − Area of the minor segment.
6. 06The unitary method underlies all sector and arc-length formulas: the full circle (360°) has area πr², so a θ° sector has area proportional to θ/360.