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Class 10th Maths || Menu
  • Important
    • Previous Year Papers 2019
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  • Real Numbers
    • Ex. 1.1 & Intro
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  • Pair of Linear Equations in 2 Variables
    • Ex. 3.1 & Intro
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  • Triangles
    • Intro & Theorem
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  • Introduction to Trigonometry
    • Ex 8.1 & Intro
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  • Some Applications of Trigonometry
    • Ex. 9.1 & Intro
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  • Circles
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  • Areas Related to Circles
    • Ex 12.1 & Intro
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  • Surface Areas and Volumes
    • Ex. 13.1 NCERT
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    • Ex. 14.1 NCERT
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  • Probability
    • Ex. 15.1 & Intro
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CBSE Class 10 Maths Chapter 12 Areas related to Circles Notes

Circumference of a circle = 2πr
Area of a circle = πr2 …[where r is the radius of a circle]
Area of a semi-circle = \frac { { \pi r }^{ 2 } }{ 2 }
Area of a circular path or ring:
Areas related to Circles Class 10 Notes Maths Chapter 12 1
Let ‘R’ and ‘r’ he radii of two circles
Then 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 enclosed by the two radii is greater than a semi-circle.
Areas related to Circles Class 10 Notes Maths Chapter 12 2
If the arc subtends angle ‘θ’ at the centre, then the
Length of minor arc = \frac { \theta }{ 360 } \times 2\pi r=\frac { \theta }{ 180 } \times \pi r
Length of major arc = \left( \frac { 360-\theta }{ 360 } \right) \times 2\pi r

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.
(i) A sector is called a minor sector if the minor arc of the circle is part of its boundary.
\hat { OAB } is minor sector.
Areas related to Circles Class 10 Notes Maths Chapter 12 3
Area of minor sector = \frac { \theta }{ 360 } \left( { \pi r }^{ 2 } \right)
Perimeter of minor sector = 2r+\frac { \theta }{ 360 } \left( { 2\pi r } \right)

(ii) A sector is called a major sector if the major arc of the circle is part of its boundary.
\hat { OACB } is major sector
Area of major sector = \left( \frac { 360-\theta }{ 360 } \right) \left( { \pi r }^{ 2 } \right)
Perimeter of major sector = 2r+\left( \frac { 360-\theta }{ 360 } \right) \left( { 2\pi r } \right)

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.
Areas related to Circles Class 10 Notes Maths Chapter 12 4
Area of Minor segment = Area of the corresponding sector – Area of the corresponding triangle
Areas related to Circles Class 10 Notes Maths Chapter 12 5

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
Area of major sector + Area of triangle
Areas related to Circles Class 10 Notes Maths Chapter 12 6
Areas related to Circles Class 10 Notes Maths Chapter 12 7

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