Notes on Circles | Grade 7 > Compulsory Maths > Geometry: Triangles, Quadrilaterals and Circles | KULLABS.COM

Circles

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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.



  • 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.
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Very Short Questions

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

 

 

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  • The straight line is drawn from the centre of a circle to a point on its circumference is called ______ .

    the diameter of a square
    the radius of the circle
    the diameter of a circle
    the radius of a square
  • The curved boundary line of a circle is called its ______ .

    circle
    circumstance
    radius
    center
  • Half part of a circle is called a ________ .

    circumstance
    diameter
    semi-circle
    radius 
  • The part of a curve between two given points on the curve of a circle is called ______ .

    an arc 
    the side
    a radius
    the edge
  • The region bounded by an arc and its corresponding chord is called ______ .

    the perimeter of the circle
    the sector
    the segment of a circle
    the radius of a circle
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