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Dallasb22

  • 3 years ago

if pa=10 and be=21 find bp

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  1. CliffSedge
    • 3 years ago
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    Is there a diagram to go with this information?

  2. Dallasb22
    • 3 years ago
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  3. CliffSedge
    • 3 years ago
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    Thank you. Can we assume AP is tangent to the circle and that BE is a diameter?

  4. Dallasb22
    • 3 years ago
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    Yes

  5. CliffSedge
    • 3 years ago
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    Well, first thing that comes to mind (because I can't remember the tangent-chord theorems off the top of my head right now..) is that you can form a right triangle AOP with O the center of the circle and AO a radius. From there you can use Pythagoras' theorem to get the missing lengths.

  6. CliffSedge
    • 3 years ago
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    It's not very direct, but will work.

  7. Dallasb22
    • 3 years ago
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    How can AOP form a right triangle? I drew the line(auxillary lines) and it appears acute.

  8. Dallasb22
    • 3 years ago
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    Angle AOP being acute.

  9. CliffSedge
    • 3 years ago
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    Yes. Angle OAP is the right angle because tangents to a circle are always at right angles to their radii.

  10. Dallasb22
    • 3 years ago
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    Oh yeah...

  11. CliffSedge
    • 3 years ago
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    I think that's the preliminary proposition that is used to prove the various tangent and chord theorems. I like this website for reviewing such things: http://www.mathwarehouse.com/geometry/circle/tangent-secant-side-length.php

  12. Dallasb22
    • 3 years ago
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    OA=10.5 correct?

  13. CliffSedge
    • 3 years ago
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    Line OEP is therefore the hypotenuse, and when you add OB=OA, you get BP. Yes, OA is a radius so is half the diameter BE.

  14. CliffSedge
    • 3 years ago
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    Oh, that's nice, everything works out to rational numbers. Very kind of them . . .

  15. Dallasb22
    • 3 years ago
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    |dw:1346780775442:dw|

  16. Dallasb22
    • 3 years ago
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    I'm still not sure how to find EP?

  17. CliffSedge
    • 3 years ago
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    I don't think you need EP, but did you use Pythagoras' theorem to get OP?

  18. Dallasb22
    • 3 years ago
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    10(^2)+10.5(^2)=c(^2) I get 210.25???

  19. Dallasb22
    • 3 years ago
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    I was going to find EP. Then add BE+EP=BP

  20. CliffSedge
    • 3 years ago
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    (take square root of c^2)

  21. Dallasb22
    • 3 years ago
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    Ahhh. 14.5 + 10.5 correct? Equaling 25

  22. CliffSedge
    • 3 years ago
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    If you use the theorem from that website I linked to, it shows the following: |dw:1346781296754:dw| Which when you simplify and put into standard form yields the quadratic equation x^2+21x-100=0. I find that unnecessary if you don't like quadratics. Either way it includes an extra step and Pythagoras' theorem gets us there just as easily.

  23. CliffSedge
    • 3 years ago
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    Yes, the solutions to that quadratic equation are x=4 and x=-25. Throw out the negative length as meaningless, and EP=4; add that to the diameter and BP=25.

  24. Dallasb22
    • 3 years ago
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    Okay good. Sometimes I just need someone to make me ask myself the right questions.

  25. Dallasb22
    • 3 years ago
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    Thanks for helping! I have another if you don't mind...?

  26. CliffSedge
    • 3 years ago
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    I usually never bother to remember such specific theorems, I prefer to deduce everything from more basic stuff that is easy to remember.

  27. CliffSedge
    • 3 years ago
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    Sure, I got time.

  28. Dallasb22
    • 3 years ago
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    Yes, and the PT is very easy.

  29. CliffSedge
    • 3 years ago
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    Exactly, it shows up everywhere; only thing you had to remember is that tangents are perpendicular to radii.

  30. Dallasb22
    • 3 years ago
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    Exactly.

  31. CliffSedge
    • 3 years ago
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    Might as well start a new thread for your next question; maybe we can get others to jump in and add their insights as well.

  32. Dallasb22
    • 3 years ago
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    Will do.

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