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

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

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

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

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

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

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

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

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

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

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

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

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