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TANGENT
CIRCLESGROUP 6III - CHARITY
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REVIEW :
A is a line
that intersects thecircle at exactly one
point called the
tangent
point of tangency
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A line segment or a
ray can be tangent
to a circle if it is apart of the line that
is tangent to the
circle
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The radius of a
circle is
perpendicular to
the point of
tangency
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TANGENT CIRCLES
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Common tangents are
lines or segments thatare tangent to more than
one circle at the sametime. It is a line that is
tangent to each of two
coplanar circles
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A common tangent can be tangent
either internally or externally.
A common internal tangent is acommon tangent that intersects the
segment that joins the center of the
two circles.
A common external tangent is a
common tangent that does notintersect the segment that joins the
centers of the two circles.
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Line L2 is a common external tangent
while line L1 is a common internal
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4 Common Tangents (2 completely separate circles)
2 external tangents (blue)
2 internal tangents (black)
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3 Common Tangents
(2 externally tangent circles)
2 external tangents (blue)
1 internal tangent (black)
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2 Common Tangents
(2 overlapping circles)
2 external tangents (blue)
0 internal tangents
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1 Common Tangent(2 internally tangent circles)
1 external tangent (blue)
0 internal tangents
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(2 concentric
circles)
Concentric circles
are circles
with the samecenter.
0 external tangents
0 internal tangents
(one circle floating
inside the other,
without touching)
0 external tangents
0 internal tangents
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The common tangent that connects thecircles will be replaced by a common
secant because it intersects a circle in
more than one point.
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Tangent circles may be tangent
either internally or externally.
Tangent circles are tangentinternally if one lies in the interior
of the other (except for the point of tangency).
Tangent circles are tangentexternally if each lies in the
exterior of the other (except for the
oint of tan enc .
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The circles areexternally tangent. The circles areinternally tangent.
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HOW TO SOLVE FOR THELENGTH OF THE COMMON
TANGENT OF THE TWOCIRCLES
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Draw the segment connecting the
centers of the two circles and draw the
two radii to the points of tangency
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From the center of the smaller circle, draw a segment
parallel to the common tangent till it hits the radius of thelarger circle.
You end up with a right triangle and a rectangle; one of
the rectangle’s sides is the common tangent.
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You now have a right triangle and a rectangle and
can finish the problem with the Pythagorean
Theorem and the simple fact that opposite sides of
a rectangle are congruent.
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