## Areas related to Circles

Circumference of a circle = 2πr

Area of a circle = πr^{2} …[where r is the radius of a circle]

Area of a semi-circle =πr^{2} /^{ }2

Area of a circular path or ring:

Let ‘R’ and ‘r’ he radii of two circles

Then area of shaded part = πR^{2} – πr^{2} = π(R^{2} – r^{2}) = 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 =

Length of major arc =

**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 =

Perimeter of minor sector =

**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

ncert solution

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