Home
Class 9
MATHS
In Figure, l is a line intersecting th...

In Figure, `l` is a line intersecting the two concentric circles, whose common centre is `O ,` at the points `A ,\ B ,\ C\ a n d\ D` . Show that `A B=C Ddot`

Text Solution

Verified by Experts

Let `OM` be perpendicular from `O \on line\ l`
We know that perpendicular from the center of the circle to as a chord :bisects the chord
since `BC` is chord of the smaller circle
`OM_|_BC`
`BM=CM`....(i)
Again `AD` is chord of the larger circle and `AM_|_AD`
`AM=DM`...(II)
subtracting from (i) and (ii), `AM-BM=DM-CM=>AB=CD`Let `OM` be perpendicular from `O` on line `l`
We know that perpendicular from the center of the circle to as a chord :bisects the chord
since `BC` is chord of the smaller circle
`OM_|_BC`
`BM=CM`....(i)
Again `AD` is chord of the larger circle and `AM_|_AD`
`AM=DM`...(II)
subtracting from (i) and (ii), `AM-BM=DM-CM=>AB=CD`
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 Figure,l is a line intersecting the two concentric circles,whose common centre is O, at the points A,B,C and D. Show that AB=CD

If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see Fig. 10.25).

In the figure, two circles with centers O and P intersect each other at points D and C. Line AB intersects the circle with centre O at points A and B and touches the circle with centre P at point E. Prove /_ADE+/_BCE=180^(@) .

In figure, two circles intersect each other at points A and E. Their common secant through E intersects the circles at points B and D. The tangents of the circles at points B and D intersect each other at point C. Prove that square ABCD is cyclic.

Given two concetric circles with centre O. A line cut the circle at A,B,C and D respectively. If AB=10cm, then find the length of CD.

Two circle with centres A and B intersect at C and D. Prove that /_ACB=/_ADB

In the adjoining figure, O is the centre of two concentric circles. The chord AB of larger circle intersects the smaller circle at C and D. (i) Find AC:BD . (ii) If AC=2cm , then find the length of BD.

In Figure,two congruent circles with centres O and O' intersect at A and B .If /_AO'B=50^(@), then find /_APB

RD SHARMA-CIRCLE -All Questions
  1. A B\ a n d\ C D are two chords of a circle such that A B=6\ c m ,\ C...

    Text Solution

    |

  2. In the figure, O D is perpendicular to the chord A B of a circle ...

    Text Solution

    |

  3. In Figure, l is a line intersecting the two concentric circles, whos...

    Text Solution

    |

  4. In a circle of radius 5\ c m ,\ A B\ a n d\ A C are two chords suc...

    Text Solution

    |

  5. In an equilateral triangle, prove that the centroid and centre of th...

    Text Solution

    |

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

    Text Solution

    |

  7. Two chords A B\ a n d\ C D of a circle are parallel and a line l is ...

    Text Solution

    |

  8. If a diameter of a circle bisects each of the two chords of a circle...

    Text Solution

    |

  9. A B\ a n d\ C D are two parallel chords of a circle whose diameter i...

    Text Solution

    |

  10. Two concentric circle with centre O have A ,\ B ,\ C ,\ D as the p...

    Text Solution

    |

  11. Two circles whose centres are O and O ' intersect at Pdot Through ...

    Text Solution

    |

  12. Prove that the line joining the mid-points of two parallel chords of a...

    Text Solution

    |

  13. Two circles of radii 10\ c m\ a n d\ 8\ c m intersect and the leng...

    Text Solution

    |

  14. Two circles of radii 5\ c m\ a n d\ 3c m intersect at two points a...

    Text Solution

    |

  15. In Figure, two circles with centres A\ a n d\ B and of radii 5\ c ...

    Text Solution

    |

  16. In Figure, hat A B~= hat A C and O is the centre of the circle. Prove...

    Text Solution

    |

  17. Prove that the right bisector of a chord of a circle, bisects the ...

    Text Solution

    |

  18. Prove that the perpendicular bisector of a chord of a circle always ...

    Text Solution

    |

  19. In Figure, A B=C B\ a n d\ O is the centre of the circle. Prove that B...

    Text Solution

    |

  20. Two circle with centres A and B intersect at C and Ddot Prove that /A ...

    Text Solution

    |