Home
Class 9
MATHS
Two equal chords A B and C D of a circle...

Two equal chords `A B` and `C D` of a circle with centre `O` , when produced meet at a point `E ,` as shown in Figure, Prove that `B E=D E` and `A E=C Edot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    RD SHARMA ENGLISH|Exercise All Questions|206 Videos
  • CONGRUENT TRIANGLE

    RD SHARMA ENGLISH|Exercise All Questions|290 Videos

Similar Questions

Explore conceptually related problems

In the figure, two equal chords AB and CD of a circle with centre O, intersect each other at E, Prove that AD=CB

In Figure, equal chords A B and C D of a circle with centre O , cut at right angles at E . If M and N are mid-point of A B and C D respectively, prove that OMEN is a square.

In Figure, equal chords A B and C D of a circle with centre O , cut at right angles at Edot If M and N are mid-point of A B and C D respectively, prove that OMEN is a square.

If two chords A B and A C of a circle with centre O are such that the centre O lies on the bisector of /_B A C , prove that A B=A C , i.e. the chords are equal.

In a circle with centre O , chords A Ba n dC D intersect inside the circumference at Edot Prove that /_A O C+/_B O D=2/_A E Cdot

In a circle with centre O , chords A B\ a n d\ C D intersect inside the circumference at E . Prove that /_A O C+\ /_B O D=2\ /_A E C

In A B C ,A D is the median through A and E is the mid-point of A D . B E produced meets A C in F (Figure). Prove that A F=1/3A Cdot

In A B C ,A D is the median through A and E is the mid-point of A D . B E produced meets A C in F (Figure). Prove that A F=1/3A Cdot

In A B C ,A D is the median through A and E is the mid-point of A D . B E produced meets A C in F (Figure). Prove that A F=1/3A C .

In Figure, A B\ a n d\ A C are two equal chords of a circle whose centre is O . If O D\ _|_A B\ a n d\ O E\ _|_A C , prove that /_\A D E is an isosceles triangle.

RD SHARMA ENGLISH-CIRCLE -All Questions
  1. If two chords of a circle are equally inclined to the diameter thro...

    Text Solution

    |

  2. In Figure, O is the centre of a circle and P O BISECTS /A P D. Prove...

    Text Solution

    |

  3. Two equal chords A B and C D of a circle with centre O , when produced...

    Text Solution

    |

  4. If two equal chords of a circle in intersect within the circle, prove ...

    Text Solution

    |

  5. If two equal chords of a circle intersect within the circle, prove t...

    Text Solution

    |

  6. prove that the line joining the mid-point of two equal chords of a ...

    Text Solution

    |

  7. L\ a n d\ M are mid-point of two equal chords A B\ a n d\ C D of a c...

    Text Solution

    |

  8. PQ and RQ are chords of a circle equidistant from the centre. Prove t...

    Text Solution

    |

  9. In the figure, two equal chords AB and CD of a circle with centre O, i...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. In Figure, equal chords A B and C D of a circle with centre O , cut at...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Bisector A D of /B A C of /\ A B C passes through the centre O of the ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |