These notes for CBSE Class 10 Mathematics, Chapter 12, focus on Areas Related to Circles. They define the area of a circle as the region enclosed by its boundary, calculated using the formula pr², and the perimeter (circumference) as the length of the boundary, calculated as 2pr, where r is the radius. The notes explain the area of a sector of a circle, which is a part enclosed by two radii and an arc, using the formula (?/360°) × ?r². The length of an arc of a sector is given by (?/360°) × 2?r. The perimeter of a minor sector is the sum of the arc length and two radii. The concept of a circular segment, divided by a chord, is introduced, with the area of a minor segment being the area of the corresponding sector minus the area of the triangle formed by the radii and the chord. The area of a major segment is the total circle area minus the minor segment area. Formulas for the area enclosed by two concentric circles and results concerning touching circles and rotating wheels are also provided. These notes are ideal for quick revision before exams.
Last optimized 10 Aug 2026
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We know that
The area of a circle is the measurement of the region enclosed by its boundary. It is measured in square units. -ie- square centimetres or square metres etc.
Area of the circle = pr2
The perimeter of a circle is the length of its boundary. The unit measurement of perimeter is the
unit of length.
Perimeter of circle = 2pr
where r is the radius of the circle.
Perimeter of a circle is known as circumference of a circle.
The part of the circle inclined between two radii (OA & OB) is called sector of circle.
Area of the sector OAPB =0 /360° x pr2
Length of an arc of sector OAPB = length of arc AB =0 /360° x 2pr
Where 0 is the measure of arc AB.
Perimeter of the sector (minor sector)
=0 /360° x 2pr + 2r
Any chord AB divides circle into two parts. The bigger part is known as major segment and smaller one is called minor segment.
Area of minor segment APB — Area of sector OAPB — area of ?OAB
Area of major segment OAQB = pr2 — area of minor segment APB.
NOTE: Area of ? OAB with ?AOB = 0 = 1/2 (OA) (OB) sin?
Area of segment of a circle = Area of the corresponding sector — Area of the corresponding triangle.
If R and r are the radii of two concentric circles such that R > r then area enclosed by the two circles = pR2 – pr2
(i) If two circles touch internally, then the distance between their centres is equal to the difference of their radii.
(ii) If two circles touch externally, then the distance between their centres is equal to the sum o their radii.
(iii) Distance moved by a rotating wheel in one revolution is equal to the circumference of the wheel.
(iv) The number of revolutions completed by a rotating wheel in one minute Distance moved in one minute= Distance moved in one minute / circumference
The area of a circle is given by the formula A = ?r², where r is the radius of the circle.
The area of a sector of a circle is calculated using the formula A = (?/360°) × ?r², where ? is the angle of the sector in degrees and r is the radius.
The length of an arc of a sector is calculated using the formula L = (?/360°) × 2?r, where ? is the angle of the sector in degrees and r is the radius.
The area of a segment of a circle is found by subtracting the area of the corresponding triangle from the area of the corresponding sector.
If R and r are the radii of two concentric circles with R > r, the area enclosed by them is ?R² – ?r².
The distance moved by a rotating wheel in one revolution is equal to its circumference.
If two circles touch internally, the distance between their centers is equal to the difference of their radii.
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