Area Related to Circles Class 10 Notes Maths Chapter 12

CHAPTER AT A GLANCE

1. Circle
The set of all points in a plane which are at a fixed distance from a fixed point in the plane is called circle. The fixed point is called centre and the fixed distance is called radius of the circle.

2. Terms Related To Circle
(I) Chord: A line segment joining any two points on a circle .
(ii) Arc: A piece of a circle between two points on the circle is called an arc.

The arc less than the semicircular arc is called minor arc and the one greater than the semi-circular arc is called major arc.

(iii) Sector : The portion of a circular region enclosed by two radii and the corresponding arc is called a sector of the circle.

Sector smaller than the semi circle is called minor sector and the sector larger than the semi-circle is called major sector.

(iv) Segment: The portion of a circular region enclosed between a chord and the corresponding arc is called a segment of the circle.

The segment bounded by the chord and the minor arc intercepted by the chord is called minor segment and the segment bounded by the chord and the major arc intercepted by the chord is called major segment.

3. Circumference and Area of a Circle
(I) The perimeter or circumference of a circle is defined as distance covered by travelling once around a circle and is given by C = 27rr = pid
where r = radius of the circle and d = diameter of the circle.
(ii) The area of a circle of radius r is given by, A=pir2 = pi/4d2
Where r = radius of the circle
d = diameter of the circle.
(iii) Area of a circular ring:
The area of the circular path or ring is given by the difference of the area of the outer circle and the area of inner circle. Area of circular ring = pi:(R2-r2)

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