# Is there any theorem that states the condition for two distinct circles to intersect at two or one points?

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?

• If 2 circles intersect at only one point, the distance between the centers equals to the sum of radii. Similar for another 2 cases. – Mythomorphic Jan 31 '17 at 16:30
• @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? – MvG Jan 31 '17 at 19:32
• @hkmather802 but this doesn't happen here postimg.org/image/jihc9lyht – Navneet Kumar Feb 26 '17 at 9:42

## 1 Answer

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 $R-r<d<R+r$

If there are no intersections, then $d>R+r$ (externally) or $d<R-r$ (internally)

• Your theorem is wrong .There is a hole in it. – Navneet Kumar Feb 26 '17 at 9:37
• postimg.org/image/jihc9lyht you can see that the theorem doesn't works in this case. – Navneet Kumar Feb 26 '17 at 9:38
• Thank you for your comment. See my fixed edition. – Mythomorphic Feb 26 '17 at 9:55
• it looks better now.Thank You for help! – Navneet Kumar Feb 26 '17 at 9:56