February 22nd, 2018, 01:58 AM  #1 
Member Joined: Dec 2017 From: Tel Aviv Posts: 48 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 12:31 PM. 
February 22nd, 2018, 02:55 AM  #2  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,541 Thanks: 516 Math Focus: Yet to find out.  Ok. Quote:
Quote:
Perhaps you can provide an example. Last edited by skipjack; February 22nd, 2018 at 12:22 PM.  
February 22nd, 2018, 03:05 AM  #3  
Senior Member Joined: Jun 2015 From: England Posts: 766 Thanks: 223  Quote:
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 rightangled triangles in this construction if you wish. Last edited by skipjack; February 22nd, 2018 at 12:31 PM.  
February 22nd, 2018, 03:08 AM  #4 
Member Joined: Dec 2017 From: Tel Aviv Posts: 48 Thanks: 3 
O.K. Thanks.

February 22nd, 2018, 03:45 AM  #5 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,541 Thanks: 516 Math Focus: Yet to find out. 
Wow.

February 22nd, 2018, 03:46 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,970 Thanks: 807 
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.

February 22nd, 2018, 04:02 AM  #7 
Member Joined: Dec 2017 From: Tel Aviv Posts: 48 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 12:29 PM. 
February 22nd, 2018, 04:56 AM  #8 
Senior Member Joined: Jun 2015 From: England Posts: 766 Thanks: 223 
1 character

February 22nd, 2018, 05:10 AM  #9 
Member Joined: Dec 2017 From: Tel Aviv Posts: 48 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 05:21 AM. 

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