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msingh

  • 3 years ago

two equal circles of radius 5 cm have two common tangent AB and CD which touch the circle on A, C and B, D respectively and if CD = 24 cm, find the length of AB.

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  1. msingh
    • 3 years ago
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    |dw:1358505912245:dw|

  2. AravindG
    • 3 years ago
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    interesting :)

  3. AravindG
    • 3 years ago
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    can i know what did you attempt here?

  4. ParthKohli
    • 3 years ago
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    can i know what was your attempt here?

  5. msingh
    • 3 years ago
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    in a traingle bcd, i apply pythagoras theorem

  6. msingh
    • 3 years ago
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    CD^2=BC^2+BD^2

  7. AravindG
    • 3 years ago
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    but how you got CD?

  8. msingh
    • 3 years ago
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    it is given

  9. msingh
    • 3 years ago
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    24^2=BC^2+5^2

  10. AravindG
    • 3 years ago
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    ok

  11. AravindG
    • 3 years ago
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    ok you see for getting AB we need to take one more triangle.can you tell which one that will be?

  12. msingh
    • 3 years ago
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    i don't know

  13. msingh
    • 3 years ago
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    1 Attachment
  14. AravindG
    • 3 years ago
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    well try to think of a triangle containing AB

  15. AravindG
    • 3 years ago
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    a right angled one

  16. msingh
    • 3 years ago
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    plse see this diagram..

  17. AravindG
    • 3 years ago
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    yep i saw

  18. msingh
    • 3 years ago
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    do u think taking a triangle BCD is right

  19. msingh
    • 3 years ago
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    okay...wait ..the other triangle be ABC.

  20. AravindG
    • 3 years ago
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    wait a sec...

  21. AravindG
    • 3 years ago
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    to make things clear join OB

  22. AravindG
    • 3 years ago
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    where O is centre

  23. msingh
    • 3 years ago
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    k

  24. AravindG
    • 3 years ago
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    in btw hw did u get bcd as rt angled ? :P

  25. msingh
    • 3 years ago
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    that's why i m saying i m wrong , we can't take tr.BCD

  26. Anuska
    • 3 years ago
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    ob n od shld b joined

  27. AravindG
    • 3 years ago
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    yeh :)

  28. AravindG
    • 3 years ago
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    join OA also

  29. AravindG
    • 3 years ago
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    i will try my best to draw that

  30. Anuska
    • 3 years ago
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    yea thn tk d triangle AOD

  31. Anuska
    • 3 years ago
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    & thn apply d theorem

  32. Anuska
    • 3 years ago
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    ad^2= oa^2+od^2

  33. AravindG
    • 3 years ago
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    @msingh i hand over this one to her :) seeya

  34. msingh
    • 3 years ago
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    k

  35. msingh
    • 3 years ago
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    vat is value of AD and OA

  36. Anuska
    • 3 years ago
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    oa is 5

  37. msingh
    • 3 years ago
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    how

  38. msingh
    • 3 years ago
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    OA is not a radius

  39. AravindG
    • 3 years ago
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    well msing we need to use property of tangents from same point i guess

  40. AravindG
    • 3 years ago
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    lemme try this on properly ...

  41. AravindG
    • 3 years ago
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    *on paper

  42. sirm3d
    • 3 years ago
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    draw a segment joining the centers.

  43. msingh
    • 3 years ago
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    |dw:1358508030734:dw|

  44. AravindG
    • 3 years ago
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    nice one @sirm3d

  45. sirm3d
    • 3 years ago
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    |dw:1358508121964:dw|

  46. AravindG
    • 3 years ago
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    isnt OO'=AB @sirm3d ?

  47. sirm3d
    • 3 years ago
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    that's right. O'O = AB

  48. AravindG
    • 3 years ago
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    ABOO' is a rectangle it seems

  49. AravindG
    • 3 years ago
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    my first attempt on this question wasnt as succesful as i thought .well this one was nice :)

  50. AravindG
    • 3 years ago
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    @msingh any doubts here?

  51. msingh
    • 3 years ago
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    when the triangle are congruent, vat after that

  52. msingh
    • 3 years ago
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    AO'=BO =5cm CD=24cm

  53. AravindG
    • 3 years ago
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    find OO' using that !!

  54. msingh
    • 3 years ago
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    CP= CD/2=24/2=12

  55. sirm3d
    • 3 years ago
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    OP=12 because the triangles O'CP and ODP are congruent

  56. msingh
    • 3 years ago
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    k

  57. sirm3d
    • 3 years ago
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    oops. i meant CP=DP =12

  58. AravindG
    • 3 years ago
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    Find OP 2OP =OO'

  59. sirm3d
    • 3 years ago
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    use pythagorean theorem to find the length of hypotenuse OP of triangle ODP

  60. msingh
    • 3 years ago
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    O'P =13cm

  61. msingh
    • 3 years ago
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    OO' = 26cm=AB

  62. sirm3d
    • 3 years ago
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    right you are!

  63. AravindG
    • 3 years ago
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    :) WELL DONE

  64. msingh
    • 3 years ago
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    thank u @AravindG and @sirm3d

  65. AravindG
    • 3 years ago
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    yw :)

  66. AravindG
    • 3 years ago
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    i liked @sirm3d novelty :P

  67. sirm3d
    • 3 years ago
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    yw.

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