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7-5Tangents

Objectives:

• To recognize tangents and use properties of tangents.

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Vocabulary

• Tangent• Point of Tangency

• Coon Tangents

• Coon !"ternal Tangents

• Coon #nternal Tangents

• Circuscribed Polygons

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$efinitions

• % line or line segent is tangent to a circle if itintersects t&e circle in e"actly one point.

• T&e point of intersection bet'een a tangentand its circle is called t&e point of tangency.

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T&eore 7-(

• #f a line is tangent to a

circle) t&en it is

 perpendicular to t&e radius

dra'n to t&e point oftangency.

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!"aple *

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T&eore 7-+

,Converse of T&eore 7-(

• #n a plane) if a line is perpendicular to a radius of a

circle at t&e endpoint on t&e circle) t&en t&e line is

tangent to t&e circle.

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!"aple

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Coon Tangents

•

% line or line segentt&at is tangent to t'o

circles in t&e sae

 plane is called a

coon tangent.

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Coon Tangents

•

Coon e"ternaltangents do not intersect

t&e segent '&ose

endpoints are t&e centers

of t&e circles.

•

Coon internaltangents intersect t&e

segent '&ose

endpoints are t&e centers

of t&e circles.

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T&eore 7-*/

• #f t'o segents frot&e sae e"terior point

are tangent to a circle)

t&en t&ey arecongruent.

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Circuscribed Polygons

• % polygon is circuscribed

about a circle if eac& side of

t&e polygon is tangent to t&e

circle.

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!"aple 0

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1oe'or2 

7-5 Worksheet