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kryton1212

In the figure, PB is a tangent to the circle at B. R is a point on AB such that RP is the angle bisector of <APB. <BAP=h and <APR=k. (a) Express <BRQ and <BQR in terms of h and k. (b) Is BQR an isos. triangle?

  • one year ago
  • one year ago

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  1. kryton1212
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    |dw:1359898971161:dw|

    • one year ago
  2. kryton1212
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    @Reaper534 would you kindly help me?

    • one year ago
  3. AravindG
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    sd|dw:1359901648939:dw| can you now express <BRQ in terms of h and k?

    • one year ago
  4. AravindG
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    @kryton1212 ?

    • one year ago
  5. kryton1212
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    <BRQ=h+k

    • one year ago
  6. kryton1212
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    why <BPQ=k?

    • one year ago
  7. AravindG
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    :) well done!

    • one year ago
  8. AravindG
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    now what about b part? Any idea ?

    • one year ago
  9. kryton1212
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    why <BQR=h+k????

    • one year ago
  10. AravindG
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    i didnt say <BQR=h+k

    • one year ago
  11. kryton1212
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    but the question ask <BQR

    • one year ago
  12. kryton1212
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    asks*

    • one year ago
  13. AravindG
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    can you tell how you got <BRQ as h+k?

    • one year ago
  14. kryton1212
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    ext. angle of triangle

    • one year ago
  15. BAdhi
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    @AravindG: <RBP is not 90 degrees since AB is not a diameter

    • one year ago
  16. AravindG
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    @BAdhi thanks for the spot ..I cant believe I fell for that mistake ! sorry for that @kryton1212

    • one year ago
  17. kryton1212
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    so what is <BQR?

    • one year ago
  18. hartnn
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    |dw:1359966959882:dw|

    • one year ago
  19. hartnn
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    for p, i saw triangle ABP and for <BRQ i saw triangle BRP

    • one year ago
  20. kryton1212
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    <BRQ=h+k (ext. angle of triangle)... let me see...

    • one year ago
  21. kryton1212
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    where is p?

    • one year ago
  22. hartnn
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    <BRQ=h+k (ext. angle of triangle) is better way :P

    • one year ago
  23. hartnn
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    p=<ABP

    • one year ago
  24. kryton1212
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    thanks:)

    • one year ago
  25. kryton1212
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    but the question is asking <BQR....

    • one year ago
  26. kryton1212
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    and why <RPB=k? AP is not a tangent

    • one year ago
  27. hartnn
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    RP is the angle bisector of <APB.

    • one year ago
  28. kryton1212
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    ok, i miss this-.-

    • one year ago
  29. shubhamsrg
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    BQR seems a bit complicated hmm

    • one year ago
  30. kryton1212
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    is BQR an isos. triangle? we need to prove that BQR is an isos. triangle

    • one year ago
  31. kryton1212
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    since the answer is also h+k..

    • one year ago
  32. shubhamsrg
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    |dw:1359969862634:dw| I am not too sure what use we make of the tangent! :|

    • one year ago
  33. kryton1212
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    i know now, <BAC=QBP=h (<s in alt segment.) therefore, <BQR=h+k (ext. angle of triangle) is it?

    • one year ago
  34. shubhamsrg
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    BAC = QBP ? How come ?

    • one year ago
  35. kryton1212
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    PB is a tangent, and <BAC=<QBR (angle in alt. segment)

    • one year ago
  36. kryton1212
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    |dw:1359970287522:dw|

    • one year ago
  37. shubhamsrg
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    P lies out side the circle, your logic is flawed.

    • one year ago
  38. kryton1212
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    but the theorem is this,....

    • one year ago
  39. shubhamsrg
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    Had P been any point on the circumference, then that'd been equal,

    • one year ago
  40. kryton1212
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    http://www.mathsrevision.net/gcse/pages.php?page=13

    • one year ago
  41. shubhamsrg
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    The condition is that AB should be a diameter.

    • one year ago
  42. shubhamsrg
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    Is it given In the ques ? That AB is diameter ?

    • one year ago
  43. kryton1212
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    not at all

    • one year ago
  44. shubhamsrg
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    Only then the theorem is valid.

    • one year ago
  45. shubhamsrg
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    Which is not the case here

    • one year ago
  46. kryton1212
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    Alternate Segment Theorem

    • one year ago
  47. shubhamsrg
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    As I said, those angles would be equal had AB been diameter.

    • one year ago
  48. shubhamsrg
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    Which is not our case.

    • one year ago
  49. kryton1212
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    are you sure? the alternate segment theorem is not about the diameter.

    • one year ago
  50. shubhamsrg
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    Wait, leme revise

    • one year ago
  51. shubhamsrg
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    Ohh I see ! It makes sense, I missed a step. Yep thats correct.

    • one year ago
  52. kryton1212
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    thanks :)))

    • one year ago
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