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CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Is there a diagram to go with this information?

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Thank you. Can we assume AP is tangent to the circle and that BE is a diameter?

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Well, first thing that comes to mind (because I can't remember the tangentchord 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.

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1It's not very direct, but will work.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.0How can AOP form a right triangle? I drew the line(auxillary lines) and it appears acute.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.0Angle AOP being acute.

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Yes. Angle OAP is the right angle because tangents to a circle are always at right angles to their radii.

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1I 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/tangentsecantsidelength.php

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Line 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.

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Oh, that's nice, everything works out to rational numbers. Very kind of them . . .

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1346780775442:dw

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.0I'm still not sure how to find EP?

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1I don't think you need EP, but did you use Pythagoras' theorem to get OP?

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.010(^2)+10.5(^2)=c(^2) I get 210.25???

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.0I was going to find EP. Then add BE+EP=BP

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1(take square root of c^2)

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.0Ahhh. 14.5 + 10.5 correct? Equaling 25

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1If 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+21x100=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.

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Yes, 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.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.0Okay good. Sometimes I just need someone to make me ask myself the right questions.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks for helping! I have another if you don't mind...?

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1I usually never bother to remember such specific theorems, I prefer to deduce everything from more basic stuff that is easy to remember.

Dallasb22
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, and the PT is very easy.

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Exactly, it shows up everywhere; only thing you had to remember is that tangents are perpendicular to radii.

CliffSedge
 2 years ago
Best ResponseYou've already chosen the best response.1Might as well start a new thread for your next question; maybe we can get others to jump in and add their insights as well.
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