Circle(Class-9,Math)

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1. The radius of a circle is 13 cm and the length of one of its chords is 10 cm. The distance of the chord from the centre is

 
 
 
 

2. A chord is at a distance of 8 cm from the centre of a circle of radius 17 cm. The length of the chord is

 
 
 
 

3. In the given figure, BOC is a diameter of a circle and AB = AC. Then, ∠ABC =

 
 
 
 

4. In the given figure, O is the centre of a circle. If ∠OAB = 40° and C is a point on the circle, then ∠ACB =

 
 
 
 

5. AB and CD are two equal chords of a circle with centre O such that ∠AOB = 80°, then ∠COD =

 
 
 
 

6. In the given figure, BOC is a diameter of a circle with centre O. If AB and CD are two chords such that AB || CD and AB = 10 cm, then CD =

 
 
 
 

7. In the given figure, AB is a chord of a circle with centre O and AB is produced to C such that BC = OB. Also, CO is joined and produced to meet the circle in D. If ∠ACD = 25°, then ∠AOD =

 
 
 
 

8. In the given figure, AB is a chord of a circle with centre O and BOC is a diameter. If OD ⊥ AB such that OD = 6 cm, then AC =

 
 
 
 

9. An equilateral triangle of side 9 cm is inscribed a circle. The radius of the circle is

 
 
 
 

10. In the given figure, ΔABC and ΔDBC are inscribed in a circle such that ∠BAC = 60° and ∠DBC = 50°. then, ∠BCD =

 
 
 
 

11. In the given figure, O is the centre of a circle. If ∠AOB = =100° and ∠AOC = 90°, then ∠BAC =

 
 
 
 

12. In the given figure, O is the centre of a circle and ∠AOC = 120°. Then, ∠BDC =

 
 
 
 

13. In the given figure, O is the centre of a circle in which ∠OAB = 20° and ∠OCB = 50°. Then, ∠AOC =

 
 
 
 

14. In the given figure, O is the centre of a circle in which ∠AOC = 100° side AB of quadrilateral OABC has been produced to D. Then, ∠CBD =

 
 
 
 

15. In the given figure, O is the centre of a circle and ∠OAB = 50°. Then, ∠BOD =

 
 
 
 

16. In the given figure, ABCD is the cyclic quadrilateral in which BC = CD and ∠CBD = 35°. Then, ∠BAD =

 
 
 
 

17. In figure, ΔABC is an equilateral triangle and ABDC is a quadrilateral then ∠BDC =

 
 
 
 

18. In figure, sides AB and AD of a quadrilateral ABCD are produced to E and F respectively. If ∠CBE = 100°, then find ∠CDF.

 
 
 
 

19. In figure, O is the centre of a circle and ∠AOB = 140°, then ∠ACB =

 
 
 
 

20. In figure, O is the centre of a circle and ∠AOB = 130°, then ∠ACB =