CBSE Class 10 Maths Notes Chapter 12 Areas related to Circles Pdf free download is part of Class 10 Maths Notes for Quick Revision. Here we have given NCERT Class 10 Maths Notes Chapter 12 Areas related to Circles. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.

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