1. KANYA VIDYALAYA DEHUGAON
Subject – Mathematics
std. 8TH
Chapter no. 5.
THE CIRCLE
Standard- 8
Subject-Maths
Unit-5. Circle

2. 5.The circle Revision. Standard- 8 Subject-Maths Unit-5. Circle PK
Point O is the centre of circle
OD is the radius of circle. B A P Q O D
Radius-The line segment joining the centre &any point on the circle is called radius.
PQ is the chord of a circle
Chord-The line segment joining any two point on the circle is called radius.
AB is the diameter of a circle
Diameter-The line segment passing through the centre of the circle is called radius.
Standard- 8
Subject-Maths
Unit-5. Circle

3. KANYA VIDYALAYA DEHUGAON
5.The circle
EXERCISE 19 B A P Q O D
Que 1.Fill in the blanks
The circle with centre O is shown alongside
1) Seg OD is a
2) Seg AB is a
3) Seg PQ is a
4) The length of the seg AB is that of seg OD.
Standard- 8
Subject-Maths
Unit-5. Circle

4. KANYA VIDYALAYA DEHUGAON
5.The circle T
EXERCISE 19 L
Que 2. D
Look at the fig alongside. C
Write the name of the centre of the circle,the radius, the chord and the diameter. R M
The name of the centre of the circle is C , radius is seg CD , chord is seg RT and diameter is seg LM
Standard- 8
Subject-Maths
Unit-5. Circle

5. KANYA VIDYALAYA DEHUGAON
5.The circle K
EXERCISE 19
Que 3.
Look at the figure alongside and write
whether the following statements
are true or false. C
1) Seg TS is not a chord . ( ) T S
2) Seg KM is a chord. ( ) M
3) Seg CK is a radius ( )
4)Seg KM is not a diameter. ( ).
Standard- 8
Subject-Maths
Unit-5. Circle

6. KANYA VIDYALAYA DEHUGAON
Distance between the centre of a circle and a chord
Look at the figure
Seg OM ⊥ chord AB O
The length of the perpendicular OM
is the distance of the point O from the chord AB A B M
Distance of the chord from the centre of a circle is length of perpendicular drawn from centre.
Standard- 8
Subject-Maths
Unit-5. Circle

7. KANYA VIDYALAYA DEHUGAON
1.The property of the perpendicular drawn from the centre to the chord M L T P
Look at the figure
Seg PT⊥ chord LM
Using the divider ,compare the
lengths of Seg LT and seg TM
We find that ɺ(LT)=ɺ(TM)
The perpendicular drawn from the centre
to a chord of a circle bisects the chord.
Standard- 8
Subject-Maths
Unit-5. Circle

8. congruent chord in the circle
KANYA VIDYALAY
congruent chord in the circle
Use a divider to compare the
lengths of the chords in figure. D C S R P
We find that,
ɺ(AB)=ɺ(CD)
∴ Chord AB ≅ Chord CD M N A B
ɺ(SR)=ɺ(MN)
∴Chord SR ≅ Chord MN
The chord having same length are congruent
Standard- 8
Subject-Maths
Unit-5. Circle

9. Use a divider to compare the lengths of seg OM and seg ON
2.The property of the distances between the centre and congruent chords of the circle
In the figure
Chord AB ≅ Chord PQ
Seg OM⊥ chord AB Q
Seg ON⊥ chord PQ
Use a divider to compare the
lengths of seg OM and seg ON O B N
What do you see? M
They are of equal length P A
ɺ(OM)=ɺ(ON)
Congruent chords in the same circle are at an equal
distance from the centre of circle.
Standard- 8
Subject-Maths
Unit-5. Circle

10. Angle made by the chord at the centre of a circle
In the figure
O is centre of circle
Chord is MN
The angle.∠MON is formed by drawing the radii OM and ON O N
Thus ,
the chord MN forms the angle , ∠ MON at the centre of the circle. M
Whether congruent chords in the same circle forms an
equal angle at the centre of a circle?
Standard- 8
Subject-Maths
Unit-5. Circle

11. Chord AB ≅ Chord CD Standard- 8 Subject-Maths Unit-5. Circle
3.The property of the angles made at the centre of the circle by congruent chords of that circle.
Chord AB ≅ Chord CD
In the figure,
The angle,∠AOB is formed by the chord AB at the centre. C D
The angle,∠COD is formed by the chord CD at the centre. O
Use a protractor to measure ∠AOB and ∠COD .
What do you see? B
∠AOB ≅ ∠COD . A
∴ Congruent chords in the same circle forms congruent angles at the centre of a circle.
Standard- 8
Subject-Maths
Unit-5. Circle

12. THANK YOU Study the solved problems in your book.
Solve the Exercise 20 carefully and show it .
THANK YOU

13. THANK YOU PRESENTED BY – Kanya Vidyalaya Dehugaon Mrs. Dalvi S.S.
B.Sc.B.Ed.
Kanya Vidyalaya Dehugaon
THANK YOU
Std - 8