Minor arc and Major Arc
An arc length is called a major arc if the arc length enclosed by the two radii is greater than a semi-circle.
Sector of a Circle and its Area
A region of a circle is enclosed by any two radii and the arc intercepted between two radii is called the sector of a circle.
Minor Segment
The region enclosed by an arc and a chord is called a segment of the circle. The region enclosed by the chord PQ & minor arc PRQ is called the minor segment.
Area of Minor segment = Area of the corresponding sector – Area of the corresponding triangle
Major Segment
The region enclosed by the chord PQ & major arc PSQ is called the major segment.
Area of major segment = Area of a circle – Area of the minor segment
The topics discussed in this chapter are as follows:
- Area of a circle
- Circumference of a circle
- Segment of a circle
- Sector of a circle
- Angle of a sector
- Length of an arc of a sector
- Area of sector of a circle
- Area of triangle
- Area of segment of a circle
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NCERT Solutions for Chapter 12: Areas Related to Circles
Also Check
Chapter 1: Real Numbers
Chapter 2: Polynomials
Chapter 3: Pair of Linear Equations in Two Variables
Chapter 4: Quadratic Equations
Chapter 5: Arithmetic Progression
Chapter 6: Triangles
Chapter 7: Coordinate Geometry
Chapter 8: Introduction to Trigonometry
Chapter 9: Some Applications of Trigonometry
Chapter 10: Circle
Chapter 11: Constructions
Chapter 13: Surface Areas and Volume
Chapter 14: Statistics
Chapter 15: Probability
Check out Frequently Asked Questions (FAQs) for Chapter 12: Areas Related to Circles
The circumference of a circle is 22 cm. Calculate the area of its quadrant (in sq. cm)
If the difference between the circumference and the radius of a circle is 37 cm, then using π = 22/7, calculate the circumference (in cm) of the circle.
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm × 7 cm. Find the area of the remaining card board.
Here r = 7/2 cm, L = 14 cm, B = 7 cm
Area of the remaining card board
= ar(rectangle) – 2(area of circle)
= L x B – 2πr2)
= 14 × 7 – 2 × 22/7 × 7/2 × 7/2
= 98 – 77 = 21 cm2