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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