class 10 chapter 12 (area related to circles) class notes

 

CBSE Class 10 Maths Notes Chapter 12 Areas related to Circles

Circumference of a circle = 2πr
Area of a circle = πr² …[where r is the radius of a circle]
Area of a semi-circle = πr22
Area of a circular path or ring:

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.

If the arc subtends angle ‘θ’ at the centre, then the
Length of minor arc = θ360×2πr=θ180×πr
Length of major arc = (360−θ360)×2πr

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.
OAB^ is minor sector.

Area of minor sector = θ360(πr2)
Perimeter of minor sector = 2r+θ360(2πr)

(ii) A sector is called a major sector if the major arc of the circle is part of its boundary.
OACB^ is major sector
Area of major sector = (360−θ360)(πr2)
Perimeter of major sector = 2r+(360−θ360)(2πr)

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
Area of major sector + Area of triangle

cbse class 10th areas realated to cirlces

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