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February 22nd, 2018, 01:58 AM   #1
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A circle between 2 points

Can you prove this or prove that this is wrong;
"There are 2 points"
There is only one circle (or in the plane - the same circle but in the opposite direction) that passes through the 2 points (if is a radius is given)?
And there is some more definition;
The radius > hypotenuse?
If it help, if not why?
And what do I need to be given (if I'm wrong) so that "only one circle pass through the 2 points?

Last edited by skipjack; February 22nd, 2018 at 12:31 PM.
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February 22nd, 2018, 02:55 AM   #2
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Quote:
Originally Posted by policer View Post
"There are 2 points"
Ok.
Quote:
Originally Posted by policer View Post
There is only one circle (or in the plane - the same circle but in the opposite direction) that passes through the 2 points (if is a radius is given)?
What do you mean the same circle but opposite direction? The title of this thread suggests the circle is between the points, but here you claim the circle passes through the points.
Quote:
Originally Posted by policer View Post
And there is some more definition;
The radius > hypotenuse?
If it help, if not why?
And what do I need to be given (if I'm wrong) so that "only one circle pass through the 2 points?
The hypotenuse of what? A triangle circumscribed in the circle?

Perhaps you can provide an example.

Last edited by skipjack; February 22nd, 2018 at 12:22 PM.
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February 22nd, 2018, 03:05 AM   #3
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Quote:
Originally Posted by policer View Post
Can you prove this or prove that this is wrong;
"There are 2 points"
There is only one circle (or in the plane - the same circle but in the opposite direction) that passes through the 2 points (if is a radius is given)?
And there is some more definition;
The radius > hypotenuse?
If it help, if not why?
And what do I need to be given (if I'm wrong) so that "only one circle pass through the 2 points?
I don't think this starts off right.

There are infinitely many circles that can be drawn in the plane between two given points, say A and B.

If you are also given the radius, there are still more than one circles passing through those two points and having a given radius.

The smallest radius circle lies on the straight line between those two points.
This is shown in green in my diagram, with radius R1

The right bisector of this line generates an infinite sequence of pairs of circles with the same radius - The blue and red circles in my diagram both with radius R2 and R2 > R1.

You could base your right-angled triangles in this construction if you wish.
Attached Images
File Type: jpg 3circles1.jpg (25.1 KB, 3 views)
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Last edited by skipjack; February 22nd, 2018 at 12:31 PM.
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February 22nd, 2018, 03:08 AM   #4
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O.K. Thanks.
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February 22nd, 2018, 03:45 AM   #5
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Wow.
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February 22nd, 2018, 03:46 AM   #6
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Given two points, P and Q, and a distance (the radius), r, with one leg of compasses on P, strike an arc with radius r. With one leg of the compasses on Q, strike an arc with radius r. Those two circles will intersect in two points, one on either side of the line through P and Q. Using those two points as center and radius r, you can construct exactly two circles that intersect at P and Q.
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February 22nd, 2018, 04:02 AM   #7
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Sorry, Country Boy. Can you divide your reply into steps, so I can follow the reply and understand what you mean? Thanks...

Can you draw more than 2 circles at point A & point B with the same radius?

Last edited by skipjack; February 22nd, 2018 at 12:29 PM.
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February 22nd, 2018, 04:56 AM   #8
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1 character
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February 22nd, 2018, 05:10 AM   #9
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O.K.

Sorry on the reply that I send. I confuse with the term "compasses" to the term "conscience". Sorry!!!
Your reply is very clear. Thanks.

Last edited by policer; February 22nd, 2018 at 05:21 AM.
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February 22nd, 2018, 05:51 AM   #10
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A circle
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