For example-There is a postulate that if two points are on OPPOSITE sides of a line, then the line segment joining the points must intersect the line, whereas if the points are on the SAME side of the line, the line segment joining them will not intersect the line. In other words, if the line does not pass BETWEEN the points, then the line segment will not intersect the line. Are there any postulate of this type for circle?
Is there any theorem that states the condition for two distinct circles to intersect at two or one points?
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geometry
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2If 2 circles intersect at only one point, the distance between the centers equals to the sum of radii. Similar for another 2 cases. – 2017-01-31
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0@hkmather802: I guess your comment is as much of an answer as there is to be had for this question. Do you want to post it as such, to get this out of the unanswered queue? – 2017-01-31
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0@hkmather802 but this doesn't happen here http://postimg.org/image/jihc9lyht – 2017-02-26
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EDITED
Denote $d$ be distance between centers and $r,R$ are the radii.
If 2 circles intersect at ONE point, then $d=R+r$ (externally) or $d=R-r$ (internally)
If 2 circles intersect at TWO point, then $R-r If there are no intersections, then $d>R+r$ (externally) or $d
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0Your theorem is wrong .There is a hole in it. – 2017-02-26
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0http://postimg.org/image/jihc9lyht you can see that the theorem doesn't works in this case. – 2017-02-26
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1Thank you for your comment. See my fixed edition. – 2017-02-26
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0it looks better now.Thank You for help! – 2017-02-26