anonymous
  • anonymous
if pa=10 and be=21 find bp
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Is there a diagram to go with this information?
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
Thank you. Can we assume AP is tangent to the circle and that BE is a diameter?

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anonymous
  • anonymous
Yes
anonymous
  • anonymous
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.
anonymous
  • anonymous
It's not very direct, but will work.
anonymous
  • anonymous
How can AOP form a right triangle? I drew the line(auxillary lines) and it appears acute.
anonymous
  • anonymous
Angle AOP being acute.
anonymous
  • anonymous
Yes. Angle OAP is the right angle because tangents to a circle are always at right angles to their radii.
anonymous
  • anonymous
Oh yeah...
anonymous
  • anonymous
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
anonymous
  • anonymous
OA=10.5 correct?
anonymous
  • anonymous
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.
anonymous
  • anonymous
Oh, that's nice, everything works out to rational numbers. Very kind of them . . .
anonymous
  • anonymous
|dw:1346780775442:dw|
anonymous
  • anonymous
I'm still not sure how to find EP?
anonymous
  • anonymous
I don't think you need EP, but did you use Pythagoras' theorem to get OP?
anonymous
  • anonymous
10(^2)+10.5(^2)=c(^2) I get 210.25???
anonymous
  • anonymous
I was going to find EP. Then add BE+EP=BP
anonymous
  • anonymous
(take square root of c^2)
anonymous
  • anonymous
Ahhh. 14.5 + 10.5 correct? Equaling 25
anonymous
  • anonymous
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.
anonymous
  • anonymous
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.
anonymous
  • anonymous
Okay good. Sometimes I just need someone to make me ask myself the right questions.
anonymous
  • anonymous
Thanks for helping! I have another if you don't mind...?
anonymous
  • anonymous
I usually never bother to remember such specific theorems, I prefer to deduce everything from more basic stuff that is easy to remember.
anonymous
  • anonymous
Sure, I got time.
anonymous
  • anonymous
Yes, and the PT is very easy.
anonymous
  • anonymous
Exactly, it shows up everywhere; only thing you had to remember is that tangents are perpendicular to radii.
anonymous
  • anonymous
Exactly.
anonymous
  • anonymous
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.
anonymous
  • anonymous
Will do.

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