**POSITIONS OF TWO CIRCLE**

**Externals**, if they do not overlap and

*the distance between their centers is greater than the sum of their radius.*No matter if they have the same or different radius.

**Externally tangent**, if they have just one common point and all other points are exterior to the other.

*The distance between their centers equals the sum of their radius*. No matter whether they have an equal or different radius

**.**

**Secants**, if they intersect at two different points and

*the distance between their centers is less than the sum of their radius*. No matter if they have the same or different radius. Two different circles cannot intersect at more than two points

**.**

**Internally tangent**, if they have a common point and all other points of one of them are interior to the other, exclusively

*. The distance between their centers is equal to the difference of their radius*. One has to have a greater radius than the other.

**Eccentric interior**, if they have no common points and

*the distance between their centers is greater than 0 and less than the difference of their radius*. One has to have a greater radius than the other.

**Concentric interiors**, if they have the same center (the distance between their centers is 0) and a different radius. They form a figure known as annulus or ring. One has to have a greater radius than the other one.

**Overlapping**, if they have the same center and the same radius.

*Actually, these two different circles are the same circle*. If two circles intersect at more than two points, they are necessarily overlapping circles.

**INNER AND OUTER TANGENTS**

Consider the case when
you have

**two**circles. Circles can be**internally**and**externally**tangent.
·
Two
circles in the same plane are

**internally tangent**if they intersect in exactly one point and the intersection of their interiors is not empty.
·
Two
circles in the same plane are

**externally tangen**t if they intersect in exactly one point and their intersection of their interiors is empty.
A
tangent of two circles is a

**common internal tangent**if the intersection of the tangent and the line segment joining the centers is not empty.
A
tangent of two circles is a

**common external tangent**if the intersection of the tangent and the line segment joining the centers is empty.For the complete paper, you can download at POSITION OF CIRCLE & INTERNAL EXTERNAL TANGETS (GRADE 8)

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