# Areas Related to Circles: Class 10 Mathematics NCERT Chapter 12

## Key Features of NCERT Material for Class 10 Mathematics Chapter 12 – Areas related to Circles

In the previous chapter 11, you all learned about Constructions. In this chapter: Areas Related to Circles chapter 12 class 10 Mathematics NCERT textbook, you will learn everything about Areas related to Circles.

### Area of a Circle

Area of a circle is πr2, where π=22/7 or ≈3.14 (can be utilized interchangeably for critical thinking purposes)and r is the radius of the circle.

π is the ratio of the circumference of a circle and its diameter.

### Circumference of a Circle

The perimeter of a circle is the distance secured by circumventing its boundary once. The perimeter of a circle is known by a unique name: Circumference, which is π times the diameter which is given by the formula 2πr

### A segment of a Circle

A circular segment is a area of a circle which is “cut off” from the remainder of the circle by a secant or a chord

### The sector of a Circle

A circle sector/sector of a circle is characterized as the area of a circle encased by an arc and two radii. The littler area is the minor sector and the larger area is the major sector.

#### Angle of a Sector

The angle of a sector is that angle which is encased between the two radii of the sector.

#### Length of an arc of a sector

The length of the arc of a sector can be found by utilizing the articulation for the circumference of a circle and the angle of the sector, utilizing the accompanying formula:

L= (θ/360°)×2πr

Where θ symbolizes the angle of the sector and r is the radius of the circle.

Circumference of a circle = 2πr

Area of a circle = πr2 … [where r is said to be the radius of a circle]

Area of a semicircle = πr2/2

#### Area of a circular path or ring:

Let ‘R’ and ‘r’ be the radii of two different circles

At that point area of shaded part = πR2 – πr2 = π(R2 – r2) = π(R + r)(R – r)

Minor arc and Major Arc: An arc length is called a major arc if the arc length encased by the two radii is greater than a semicircle.

In the event that the arc subtends angle ‘θ’ at the middle, at that point the

Length of minor arc =

Length of major arc =

The sector of a Circle and its Area

An area of a circle is encased by any two radii and the arc blocked between two radii is called the sector of a circle.

(I) A sector is called a minor sector if the minor arc of the circle is part of its boundary that enclosed that particular sector.

A minor sector.

Area of minor sector =

Perimeter of minor sector =

(ii) A sector is a major sector if the major arc of the circle is part of its boundary.

Area of major sector =

Perimeter of major sector =

Minor Segment: The area enclosed by an arc and a chord is called a segment of the circle. The area enclosed by the chord PQ and minor arc PRQ is called the minor segment.

Area of Minor segment is eqault to Area of the comparing sector – Area of the relating triangle

Major Segment: The area encased by the chord PQ and major arc PSQ is called the major segment.

Area of major segment  is equal to Area of a circle – Area of the minor segment

Area of major sector + Area of triangle

September 9, 2020