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SMP 1 KUDUS


 Circle

MATHEMATICS

   GRADE : 8
S
Circle in daily life                                Q
Circle in music                          Q
                             Ch    ord P
Circle in sports
                       P
Circle
Centre                               Diameter DE
                     D                                        E
Circumference                          M     O
Circular region                      O       Centre
                                 u s
                              di
Radius                     Ra
Diameter                                            F
                         M
Chord
                                                           RE
Arc                                        G          A rc
Sector
Semicircle
Segments of a circle
Crossword
A circle




BACK
Many musical instruments have a circular surface.
                       For example:




              Bingo Drum                Tabla




BACK          Snare Drum              Bass Drum
A circle



BACK              Five rings in the logo of Olympic games
A circle is a closed curve in a plane.




A circle can be drawn with the help of a circular object.
 For example: A circle drawn with the help of a coin.

                                                       BACK
A circle is a closed curve
           consisting of all points
                        A circle
           in a plane which are at the
           same distance (equidistant)
           from a fixed point inside it.
Centre O

           This fixed point (equidistant)
           inside a circle is called centre.



           A circle has one and only one
           centre.

                                    BACK
A



                             Centre
                                                 A circle
                               O




The distance around a circle is called its circumference.
Formula of circumference: C = π d C = 2 π r                 BACK
A circle divides a plane into three parts.



                                       3. Exterior of a circle

                    Centre
                      O
           2. Interior of a circle

                                     1. The circle
A plane
The interior of a circle together with its circumference
is called the circular region.                           BACK
O Centre
                            i us
                     R ad


                M
      A point on the circle

A line segment that joins any point on the circle to its centre is
                        called a radius.
                                                       (Contd…)
(Contd…)




                                                 N
                       Centre    O

                                  u   s
                               di                 M
                          Ra
                   K
                                          L
 Radii ( plural of radius) of a circle are equal in length.

 Infinite number of radius can be drawn in a circle.
                                                               BACK
A




                             O Centre
                                                A circle
                   Diameter AB




                                B
A line segment that joins any two points on the circle and passes
            through its centre is called a diameter.
                                                       (Contd…)
(Contd…)
                               M
                    A

                                                 A circle
               P

                            O
                          Centre
                                                Q


                                           B

                                   N
 Infinite number of diameters can be drawn in a circle.

 As the radii of a circle are equal in length, its diameters too
  are equal in length.
(Contd…)




                           Diameter MN
           M                                        N
                   Radius OM    O       Radius ON
                               Centre




             Radius OM = Radius ON
      Diameter MN = Radius OM + Radius ON
  The length of the diameter of a circle is twice the length of its
                             radius.
                                                            BACK
A is a point on the                           B is another point
circle                                        on the circle
               A
                   A line seCment th
                            g hord at joins   B
                         point A and B

                                O




A line segment that joins any two points on the circle is called a
                             chord.
M
              Cho
                 rd M
                     N         N
                 O
 C                                D
            Chord CD
           Diameter CD

                              K
                       L
                Chord K
       L


Diameter is also a chord of the circle.

                                      (Contd…)
M                     N
          Chord MN

               O
 C                             D
          Diameter CD


     K                    L
           Chord KL

C                              D
     M                    N

The diameter is the longest chord.
                                     (Contd…)
M                             N
                         Chord MN
         G
              Ch              O   Centre
                   or
                     d
                         GH
                                               K
          L
                     Chord KL
                                           H


Infinite number of chords can be drawn in a circle.

                                                   BACK
K                         L


                    O
                   Centre




An arc is the distance between any two points on the
              circumference of a circle.
                                               (Contd…)
Naming an arc
                                X
                          Arc KXL
                 K                         L


                           O
                           Centre




An arc is named by three points, of which two are the end points
        of the arc and the third one lies in between them.
                   Formula of Arc length: θ/360 * πd
                                                        (Contd…)
X
    Minor Arc KXL
              K                               L


                            O
                            Centre

                                                  Major Arc KYL


                               Y
An arc divides the circle into two parts: the smaller arc is called
the minor arc, the larger one is called the major arc.
                                                        (Contd…)
An arc




An arc



 BACK
X
   K                         L


             O
            Centre




Formula of Area sector: θ/360 * πr2
                                      BACK
S             Semicircle DSE
                                                Arc DSE


                            Diameter
              D                                  E
                                O
                              Centre


                                R              Semicircle DRE
                                                 Arc DRE

 Half of a circle is called a semicircle.

 A semicircle is also an arc of the circle.          (Contd…)
Semicircle DSE


         Semicircular region
                 O Diameter      E
   D
                Centre

         Semicircular region
                               Semicircle DRE


The diameter of a circle divides it into
       2 semicircular regions.
                                           BACK
S
                                             Minor segment of a circle

                 D                               E
                             Chord DE



                        Centre
                                 O
                     Major segment of a circle




                                     R
A chord divides the circular region into 2 parts, each of which is
called a segment of the circle.                         (Contd…)
P            Minor arc DPE

                 D                          E   Minor segment of
                          Chord DE                  the circle



                      Centre
                               O
                     Major segment of the
                             circle
 Major arc DQE
                          Q

 The part of the circular region enclosed by a minor arc and
                                                major
  the chord is called a minor segment.
                        major
 Minor segment does not the centre of the circle. circle.
  Major         contains contain the centre of the
                                                            BACK
O
                    Centre




                                   Semi
Radius   Diameter   Chord    Arc   Circle
O Centre
                           s OM
                       u
                  di
               Ra

           M


                                                     Semi
Radius   Diameter                 Chord        Arc   Circle
Diameter DE
         D                      E
                      O
                    Centre




                                    Semi
Radius   Diameter    Chord    Arc   Circle
Q
                            Q
                Ch o rd P
         P

                        O
                     Centre




                                          Semi
Radius   Diameter     Chord         Arc   Circle
E
                     O
                    Centre
                                     R
                                   PQ
                             Arc         F

                     G

                                                 Semi
Radius   Diameter   Chord                Arc     Circle
S
                                  Semicircle DSE

                    Semicircle
                Diameter
         D                         E
                        O
                      Centre
                    Semicircle




                                           Semi
Radius   Diameter     Chord      Arc       circle
2C
  1A                                       Across:
           4D I     A   M   E   T   E 3R   4. The line segment that joins any
   R                                  A        two points on the circle and
               R
                                               passes through its centre.
  5C   I   R   C    L   E             D    5. A closed curve in a plane.
                                           6. All points on the circle are
               U                      I       equidistant from this point.
               M                           7. A line segment that joins any
                                      U
                                               two points on a circle.
               F                      S
               E
                                      Down
6C E   N   T   R    E                 1. The distance between any two
                                         points on the circumference of the
               E                         circle.
               N                      2. The distance around the circle.

               7C H     O   R   D     3. The distance from the centre of the
                                         circle to a point on the circle.
               E
Circle

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Circle

  • 1. SMP 1 KUDUS Circle MATHEMATICS GRADE : 8
  • 2. S Circle in daily life Q Circle in music Q Ch ord P Circle in sports P Circle Centre Diameter DE D E Circumference M O Circular region O Centre u s di Radius Ra Diameter F M Chord RE Arc G A rc Sector Semicircle Segments of a circle Crossword
  • 4. Many musical instruments have a circular surface. For example: Bingo Drum Tabla BACK Snare Drum Bass Drum
  • 5. A circle BACK Five rings in the logo of Olympic games
  • 6. A circle is a closed curve in a plane. A circle can be drawn with the help of a circular object. For example: A circle drawn with the help of a coin. BACK
  • 7. A circle is a closed curve consisting of all points A circle in a plane which are at the same distance (equidistant) from a fixed point inside it. Centre O This fixed point (equidistant) inside a circle is called centre. A circle has one and only one centre. BACK
  • 8. A Centre A circle O The distance around a circle is called its circumference. Formula of circumference: C = π d C = 2 π r BACK
  • 9. A circle divides a plane into three parts. 3. Exterior of a circle Centre O 2. Interior of a circle 1. The circle A plane The interior of a circle together with its circumference is called the circular region. BACK
  • 10. O Centre i us R ad M A point on the circle A line segment that joins any point on the circle to its centre is called a radius. (Contd…)
  • 11. (Contd…) N Centre O u s di M Ra K L  Radii ( plural of radius) of a circle are equal in length.  Infinite number of radius can be drawn in a circle. BACK
  • 12. A O Centre A circle Diameter AB B A line segment that joins any two points on the circle and passes through its centre is called a diameter. (Contd…)
  • 13. (Contd…) M A A circle P O Centre Q B N  Infinite number of diameters can be drawn in a circle.  As the radii of a circle are equal in length, its diameters too are equal in length.
  • 14. (Contd…) Diameter MN M N Radius OM O Radius ON Centre Radius OM = Radius ON Diameter MN = Radius OM + Radius ON The length of the diameter of a circle is twice the length of its radius. BACK
  • 15. A is a point on the B is another point circle on the circle A A line seCment th g hord at joins B point A and B O A line segment that joins any two points on the circle is called a chord.
  • 16. M Cho rd M N N O C D Chord CD Diameter CD K L Chord K L Diameter is also a chord of the circle. (Contd…)
  • 17. M N Chord MN O C D Diameter CD K L Chord KL C D M N The diameter is the longest chord. (Contd…)
  • 18. M N Chord MN G Ch O Centre or d GH K L Chord KL H Infinite number of chords can be drawn in a circle. BACK
  • 19. K L O Centre An arc is the distance between any two points on the circumference of a circle. (Contd…)
  • 20. Naming an arc X Arc KXL K L O Centre An arc is named by three points, of which two are the end points of the arc and the third one lies in between them. Formula of Arc length: θ/360 * πd (Contd…)
  • 21. X Minor Arc KXL K L O Centre Major Arc KYL Y An arc divides the circle into two parts: the smaller arc is called the minor arc, the larger one is called the major arc. (Contd…)
  • 23. X K L O Centre Formula of Area sector: θ/360 * πr2 BACK
  • 24. S Semicircle DSE Arc DSE Diameter D E O Centre R Semicircle DRE Arc DRE  Half of a circle is called a semicircle.  A semicircle is also an arc of the circle. (Contd…)
  • 25. Semicircle DSE Semicircular region O Diameter E D Centre Semicircular region Semicircle DRE The diameter of a circle divides it into 2 semicircular regions. BACK
  • 26. S Minor segment of a circle D E Chord DE Centre O Major segment of a circle R A chord divides the circular region into 2 parts, each of which is called a segment of the circle. (Contd…)
  • 27. P Minor arc DPE D E Minor segment of Chord DE the circle Centre O Major segment of the circle Major arc DQE Q  The part of the circular region enclosed by a minor arc and major the chord is called a minor segment. major  Minor segment does not the centre of the circle. circle. Major contains contain the centre of the BACK
  • 28. O Centre Semi Radius Diameter Chord Arc Circle
  • 29. O Centre s OM u di Ra M Semi Radius Diameter Chord Arc Circle
  • 30. Diameter DE D E O Centre Semi Radius Diameter Chord Arc Circle
  • 31. Q Q Ch o rd P P O Centre Semi Radius Diameter Chord Arc Circle
  • 32. E O Centre R PQ Arc F G Semi Radius Diameter Chord Arc Circle
  • 33. S Semicircle DSE Semicircle Diameter D E O Centre Semicircle Semi Radius Diameter Chord Arc circle
  • 34. 2C 1A Across: 4D I A M E T E 3R 4. The line segment that joins any R A two points on the circle and R passes through its centre. 5C I R C L E D 5. A closed curve in a plane. 6. All points on the circle are U I equidistant from this point. M 7. A line segment that joins any U two points on a circle. F S E Down 6C E N T R E 1. The distance between any two points on the circumference of the E circle. N 2. The distance around the circle. 7C H O R D 3. The distance from the centre of the circle to a point on the circle. E