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kryton1212

  • 2 years ago

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?

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  1. kryton1212
    • 2 years ago
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    |dw:1359898971161:dw|

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

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

  4. AravindG
    • 2 years ago
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    @kryton1212 ?

  5. kryton1212
    • 2 years ago
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    <BRQ=h+k

  6. kryton1212
    • 2 years ago
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    why <BPQ=k?

  7. AravindG
    • 2 years ago
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    :) well done!

  8. AravindG
    • 2 years ago
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    now what about b part? Any idea ?

  9. kryton1212
    • 2 years ago
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    why <BQR=h+k????

  10. AravindG
    • 2 years ago
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    i didnt say <BQR=h+k

  11. kryton1212
    • 2 years ago
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    but the question ask <BQR

  12. kryton1212
    • 2 years ago
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    asks*

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

  14. kryton1212
    • 2 years ago
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    ext. angle of triangle

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

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

  17. kryton1212
    • 2 years ago
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    so what is <BQR?

  18. hartnn
    • 2 years ago
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    |dw:1359966959882:dw|

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

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

  21. kryton1212
    • 2 years ago
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    where is p?

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

  23. hartnn
    • 2 years ago
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    p=<ABP

  24. kryton1212
    • 2 years ago
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    thanks:)

  25. kryton1212
    • 2 years ago
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    but the question is asking <BQR....

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

  27. hartnn
    • 2 years ago
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    RP is the angle bisector of <APB.

  28. kryton1212
    • 2 years ago
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    ok, i miss this-.-

  29. shubhamsrg
    • 2 years ago
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    BQR seems a bit complicated hmm

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

  31. kryton1212
    • 2 years ago
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    since the answer is also h+k..

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

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

  34. shubhamsrg
    • 2 years ago
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    BAC = QBP ? How come ?

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

  36. kryton1212
    • 2 years ago
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    |dw:1359970287522:dw|

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

  38. kryton1212
    • 2 years ago
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    but the theorem is this,....

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

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

  41. shubhamsrg
    • 2 years ago
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    The condition is that AB should be a diameter.

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

  43. kryton1212
    • 2 years ago
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    not at all

  44. shubhamsrg
    • 2 years ago
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    Only then the theorem is valid.

  45. shubhamsrg
    • 2 years ago
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    Which is not the case here

  46. kryton1212
    • 2 years ago
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    Alternate Segment Theorem

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

  48. shubhamsrg
    • 2 years ago
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    Which is not our case.

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

  50. shubhamsrg
    • 2 years ago
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    Wait, leme revise

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

  52. kryton1212
    • 2 years ago
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    thanks :)))

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