My Math Forum A circle between 2 points
 User Name Remember Me? Password

 Geometry Geometry Math Forum

 February 22nd, 2018, 02:58 AM #1 Banned Camp   Joined: Dec 2017 From: Tel Aviv Posts: 87 Thanks: 3 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 01:31 PM.
February 22nd, 2018, 03:55 AM   #2
Senior Member

Joined: Feb 2016
From: Australia

Posts: 1,737
Thanks: 606

Math Focus: Yet to find out.
Quote:
 Originally Posted by policer "There are 2 points"
Ok.
Quote:
 Originally Posted by policer 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 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 01:22 PM.

February 22nd, 2018, 04:05 AM   #3
Senior Member

Joined: Jun 2015
From: England

Posts: 891
Thanks: 269

Quote:
 Originally Posted by policer 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
 3circles1.jpg (25.1 KB, 3 views)

Last edited by skipjack; February 22nd, 2018 at 01:31 PM.

 February 22nd, 2018, 04:08 AM #4 Banned Camp   Joined: Dec 2017 From: Tel Aviv Posts: 87 Thanks: 3 O.K. Thanks.
 February 22nd, 2018, 04:45 AM #5 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,737 Thanks: 606 Math Focus: Yet to find out. Wow.
 February 22nd, 2018, 04:46 AM #6 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 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. Thanks from policer
 February 22nd, 2018, 05:02 AM #7 Banned Camp   Joined: Dec 2017 From: Tel Aviv Posts: 87 Thanks: 3 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 01:29 PM.
 February 22nd, 2018, 05:56 AM #8 Senior Member   Joined: Jun 2015 From: England Posts: 891 Thanks: 269 1 character
 February 22nd, 2018, 06:10 AM #9 Banned Camp   Joined: Dec 2017 From: Tel Aviv Posts: 87 Thanks: 3 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 06:21 AM.
 February 22nd, 2018, 06:51 AM #10 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,608 Thanks: 954

 Tags circle, points

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post guru123 Algebra 2 June 24th, 2012 05:59 AM guru123 Algebra 18 June 22nd, 2012 02:38 PM zolden Advanced Statistics 3 February 2nd, 2009 12:54 PM Oxymoron Algebra 4 July 23rd, 2008 05:11 PM karel747 Algebra 4 May 26th, 2008 02:40 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top