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: 

Areas related to Circles 

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. 

Minor arc and Major Arc

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

Length of minor arc = Length of minor arc

Length of major 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. 

Areas Related to Circles

A minor sector. 

Area of minor sector =  Area of minor sector

Perimeter 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 =  Areas Related to Circles

Perimeter of major sector = Areas Related to Circles

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 And Minor segment

11-7

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 triangle12-5

Areas Related to Circles

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