Home
Class 9
MATHS
A ,\ B ,\ C ,\ D are four consecutive...

`A ,\ B ,\ C ,\ D` are four consecutive points on a circle such that `A B=C Ddot` Prove that `A C=B D`

Text Solution

Verified by Experts

Given: AB=CD
Solution: As we know that equal chords cut off equal arcs in equal circles.
So, `AB=CD`
`AB+BC=BC+CD`
arc ABC=arc BCD
chord AC=chord BD
`therefore` AC=BD` Hence proved.
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

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M B Cdot Prove that: a r\ (\ L B C)=\ a r\ (\ M B C)

A B C D is a parallelogram. E is a point on B A such that B E=2\ E A\ a n d\ F is a point on D C such that D F=2\ F Cdot Prove that A E\ C F is a parallelogram whose area is one third of the area of parallelogram A B\ C Ddot

A B C is a triangle. D is a point on A B such that D=1/4A B\ a n d\ E is a point on A C such that A E=1/4A Cdot Prove that D E=1/4B C

In Figure, it is given that A B=B C and A D=E C . Prove that A B E~=C B D

A B C D is a parallelogram. P is a point on A D such that A P=1/3\ A D\ a n d\ Q is a point on B C such that: C Q=1/3B Cdot Prove that A Q C P is a parallelogram.

A B\ a n d\ C D are two chords of a circle such that A B=6\ c m ,\ C D=12\ c m\ a n d\ A B C Ddot If the distance between A B\ a n d\ C D is 3\ c m , find the radius of the circle.

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F Cdot Prove that: a r\ (\ E B G)=a r\ (\ E F C)

Let A ,B ,C ,D be four concyclic points in order in which A D : A B=C D : C Bdot If A ,B ,C are repreented by complex numbers a ,b ,c representively, find the complex number associated with point Ddot

A B and C D are two chords of a circle such that A B=6c m ,C D=12c m and A B C Ddot If the distance between A B and C D is 3c m , find the radius of the circle.

In Figure, A N and C P are perpendicular to the diagonal B D of a parallelogram A B C Ddot Prove that : A D N~= C B P (ii) A N=C P

RD SHARMA-CIRCLE -All Questions
  1. PQ and RQ are chords of a circle equidistant from the centre. Prove t...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |