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In lugnet.off-topic.fun, Dave Schuler writes:
> Since I haven't had geometry in a zillion years, I'm ill-equipped to solve a
> little dilemma I've run across, and I thought a few of the more math-minded
> among us might be able to help. Here goes:
>
> Given two points on a circle, can one compute the diameter of the circle if
> the distance between the two points is known? How would one do so?
> In the name of mercy, please keep it simple in accordance with my mathless
> brain, but I appreciate any help you folks can give!
[x-post and f.u.t. to off-topic.geek since this could get complicated]
Well, I have a B.A. in math, but I think this should be a simple enough
answer: you can't.
The main explanation is that it generally takes three distinct points to
determine a unique circle. You can get away with two distinct points only if
you know something else about them, like that they're endpoints of the
diameter.
But just knowing the distance between them isn't enough. For any two points
you can construct a infinite number of circles that pass through both of
them. The diameter of any of these circles will be greater or equal to the
distance between the two points. It will be equal when the two points _are_
the endpoints of the diameter of the circle (as mentioned above).
These circles can also be drawn with the center of the circle on either side
of the line connecting the two points. Except when the two points are
endpoints of the diameter, of course.
I hope this helps. If I've written something confusing, I can try to
simplify. Let me know. If you can provide more information, I'll certainly
try.
John Gramley
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Message has 2 Replies:
 | | Re: Here's looking at Euclid
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| (...) Yeah, I was afraid of that. Believe it or not, almost immediately after I posted I was sitting at a circular table with a can of Coke, and I realized that the same 1 1/2 inch that defines the diameter of the can only describes a tiny portion (...) (24 years ago, 1-Aug-00, to lugnet.off-topic.geek)
| | | Re: Here's looking at Euclid
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| (...) Hmm... That was my first instinct reaction, however, the thought occurred that perhaps what is known about the two points is their distance apart as measured along the circumfrence of the circle? (assuming closest distance, but furthest would (...) (24 years ago, 1-Aug-00, to lugnet.off-topic.geek)
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Message is in Reply To:
| | Here's looking at Euclid
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| Since I haven't had geometry in a zillion years, I'm ill-equipped to solve a little dilemma I've run across, and I thought a few of the more math-minded among us might be able to help. Here goes: Given two points on a circle, can one compute the (...) (24 years ago, 1-Aug-00, to lugnet.off-topic.fun)
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