Home
Class 9
MATHS
Show that if two chords of a circle bise...

Show that if two chords of a circle bisect one another they must be diameters.

Text Solution

Verified by Experts

Proof: In `triangleAOC` and `triangleBOD`
`angleAOC=angleBOD`
`OA=OB`
`OC=OD`
`triangleAOC~=triangleBOD` (By SAS)
Now, AC=BD ____1
In `triangleAOD` and `triangleBOC`
`angleAOD=angleBOC`
...
Promotional Banner

Topper's Solved these Questions

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    RD SHARMA|Exercise All Questions|205 Videos
  • CONGRUENT TRIANGLE

    RD SHARMA|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

AC and BD are chords of a circle that bisect each other.Prove that: AC and BD are diameters ABCD is a rectangle.

Is every chord of a circle also a diameter?

If a diameter of a circle bisects each of the two chords of a circle,prove that the chords are parallel.

If a diameter of a circle bisects each of the two chords of a circle,prove that the chords are parallel.

Prove that, if a diameter of a circle bisects two chords of the circle then those two chords are parallel to each other.

AC and BD are chords of a circle which bisect each other.Prove that (i) AC and BD are diameters (ii) ABCD is a rectangle.

AC and BD are chords of a circle which bisect each other.Prove that (i) AC and BD are diameters (ii) ABCD is a rectangle

AC and BD are chords of a circle which bisect each other.Prrove that (i) AC and BD are diameters,(ii) ABCD is a rectangle

RD SHARMA-CIRCLE -All Questions
  1. In the figure, two equal chords AB and CD of a circle with centre O, i...

    Text Solution

    |

  2. A ,\ B ,\ C ,\ D are four consecutive points on a circle such that ...

    Text Solution

    |

  3. Show that if two chords of a circle bisect one another they must be ...

    Text Solution

    |

  4. In Figure, equal chords AB and CD of a circle with center O , cut at r...

    Text Solution

    |

  5. Two equal circles intersect in P and Q . A straight line through P mee...

    Text Solution

    |

  6. Prove that all the chords of a circle through a given point within it,...

    Text Solution

    |

  7. Prove that the diameter is the greatest chord in a circle.

    Text Solution

    |

  8. Bisector A D of /B A C of A B C passes through the centre O of the ci...

    Text Solution

    |

  9. In Figure, A B\ a n d\ A C are two equal chords of a circle whose c...

    Text Solution

    |

  10. In Figure, O A and O B ar respectively perpendiculars to chords C D an...

    Text Solution

    |

  11. Three girls Reshma, Salma and Mandip are playing a game by standing...

    Text Solution

    |

  12. A circular park of radius 20m is situated in a colony. Three boys A...

    Text Solution

    |

  13. In Figure, calculate the measure of /A O Cdot

    Text Solution

    |

  14. A , B and C are three points on a circle such that the angles subten...

    Text Solution

    |

  15. In Figure., A B C is a triangle in which /B A C=30^0dot Show that B C ...

    Text Solution

    |

  16. A chord of a circle is equal to the radius of the circle find the angl...

    Text Solution

    |

  17. In Figure, /A B C=69^0,\ /A C B=31^0 , find /B D C

    Text Solution

    |

  18. In Figure, /P Q R=100^0, where P ,\ Q\ a n d\ R are points on a circle...

    Text Solution

    |

  19. In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD...

    Text Solution

    |

  20. BC is a chord with centre O. A is a point on an arc BC . Pr...

    Text Solution

    |