Circles

Subject: Compulsory Maths

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Overview

The plane figure bounded by a curved line and every point of the line which is equidistance from a fixed point called the centre of the circle.The curved boundary line of a circle sis called its circumstance. The straight line is drawn from the centre of a circle to a point on its circumference is called the radius of the circle.
Circles

Circle and its different parts

source :cnx.org Fig :circle
source :cnx.org
Fig :circle

A circle is a plane figure bounded by a curved line and every point of the line is equidistance from a fixed point called the centre of the circle.

  1. Circumference of circle
    The curved boundary line of a circle sis called its circumstance. The length of the circumference represents the perimeter of the circle.
  2. Radius of a circle
    The straight line is drawn from the centre of a circle to a point on its circumference is called the radius of the circle.
    In the given figure, OA is the radius.
  3. Chord of a circle
    The straight line segment that joins any two points on the circumference of a circle is called the chords of a circle.
    In the given figure, AB is the chord of the circle.
  4. Diameter of a circle
    The chord that passes through the centre of a circle is called the diameter of the circle. Diameter is also called the largest chord of any circle. In the given figure, CD is the diameter of a circle. The length of the diameter of a circle is two times its radius.
    \(\therefore\) Diameter = 2 × radius
  5. Sector of a circle
    The region inside a circle bounded by its two radii (plural of radius is radii) is called sector.
    In the figure, the shaded region AOB is the sector.
  6. Arc of a circle
    The part of a curve between two given points on the curve of a circle is called an arc.
    In the figure, AB is the arc.
  7. Segment of a circle
    The region bounded by an arc and its corresponding chord is called the segment of a circle.
    In the given figure, the shaded region represents a segment.
  8. Semi-circle
    Half part of a circle is called a semi-circle. A diameter divides a circle into two halves and each half is the semi-circle.
    In the given figure, ABC is a semi-circle.

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Things to remember
  • The length of the circumference represents the perimeter of the circle.
  • The length of the diameter of a circle is two times its radius.
  • Half part of a circle is called a semi-circle.
  • It includes every relationship which established among the people.
  • There can be more than one community in a society. Community smaller than society.
  • It is a network of social relationships which cannot see or touched.
  • common interests and common objectives are not necessary for society.
Videos for Circles
Circles Radius Diameter & Pi Song – Learn Geometry – Learning
Math Antics - Circles, Circumference And Area
Math Antics - Circles, What Is PI?
Questions and Answers
Fig: Circle
Fig: Circle

A circle is a plane figure bounded by a curved line and every point of the line is equidistance from a fixed point called centre of the circle.

The different parts of a circle are:

f

Fig: Parts of Circle
  1. Circumference of a circle
  2. Radius of a circle
  3. Chord of a circle
  4. Diameter of a circle
  5. Sector of a circle
  6. Arc of a circle
  7. Segment of a circle
  8. Semi-circle 

Solution:

Centre of figure a) = O

Centre of figure b) = P

Centre of figure c) = A

Solution:

Figure a) = radii OA and OB, sector OAXB and arc AXB

Figure b) = segment CDY and Chord CD

Figure c) = semi-circle MYN and MXN, diameter MN

Solution:

Angle Opposite Arc
\(\angle\)ABC AXC
\(\angle\)PQR PYR
\(\angle\)KLM, \(\angle\)KNM, \(\angle\)LKN, \(\angle\)LMN KPM, LN
\(\angle\)ABC, \(\angle\)ADC, \(\angle\)BAD, \(\angle\)BCD AEC, BD

Solution:

Centre and Radii of figure a) = OA and OB 

Centre and Radii of figure  b) = CP and DP

Centre and Radii of figure c) = EQ and FQ

Centre and Radii of figure d) = KM and KN

Angle Opposite Arc
\(\angle\)AOB AXB
\(\angle\)CPD CYD
\(\angle\)EQF EZF
\(\angle\)MKN MSN

 

 

The straight line drawn from the centre of a circle to a point on its circumference is called the radius of a circle whereas the chord that passes through the centre of a circle is called the diameter of a circle.

The straight line segment that joins any two points on the circumference of a circle is called the chord of a circle. However, The region bounded by an arc and its corresponding chord is called the segment of a circle.

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