Position of Two Circle & Internal External Tangents


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 tangent 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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