If secant and the tangent of a circle intersect at a point outside the circle then prove that the area of the rectangle formed by the two line segments corresponding to the secant is equal to the area of the square formed by the line segment corresponding to the tangent
I find this question highly confusing. I do not know what this means. If you could please explain that to me and solve it if possible.
Circle geometry: nonparallel tangent and secant problem
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$\begingroup$
geometry
circles
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0Do you have any thoughts at all about the question?? – 2012-12-21
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1I decided to change the title ("How do I solve this?") to something that distinguishes it from the other 50,000+ questions. Please always use an informative, descriptive title. That is, unless you are trying to camouflage your question from being seen. – 2012-12-21
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0I don't understand: e have a secant and a tangent to a given circle: what "rectangle forme by the two segment corresponding to the secant" are we talking about here?? Is that perhaps the *cord* and the exterior part of the secant or what? – 2012-12-21
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0So far I'm the only one who's up-voted this question or the answers other than my own. – 2012-12-22
2 Answers
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The best reading I can find is suggested by DonAntonio. We are asked to prove $|AB|^2=|AC||AD|$

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0Is there any reason that you chose AD over CD? I think Don and I were referring to CD. I suppose knowing the solution to the problem would clear this question up, of course... – 2012-12-21
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0@rschwieb: because it is not true with CD. Imagine the secant rotating to become very close to the tangent. CD gets very small and AC gets close to AB. But you have some hope with AD-both AD and AC get close to AB. – 2012-12-21
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0OK, that's the "knowing the solution" component I was referring to. This is really not possible to guess from the OP... – 2012-12-21
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Others have answered this, but here is a source of further information:
http://en.wikipedia.org/wiki/Power_of_a_point
Here's a problem in which the result is relied on:
The result goes all the way back (23 centuries) to Euclid (the first human who ever lived, with the exception of those who didn't write books on geometry that remain famous down to the present day):
http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII36.html
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1Very cool. That is a very interesting distinction you give to Euclid, as well :) – 2012-12-21