14 2 tangents to a circle lesson
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Use Properties of Tangents
14-2
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Vocabulary
• Circle- the set of all pts in a plane that are equidistant from a given pt. called the center of the circle.
• Radius- segment whose endpoints are the center and any point on the circle
• Diameter- a chord that contains the center of the circle.
• Two polygons are similar if corresponding angles are congruent and corresponding side lengths are proportional. ΔABC ΔDEF
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P
P is the center of the circle
A
BSegment AB is a diameter
C
Segments AP, PB, and PC are radii
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Chord• Chord- a segment whose endpoints are on
the circle.
A B
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Secant
• Secant- a line that intersects a circle in 2 pts
A
B
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Tangent
• Tangent- a line in the plane of the circle that intersects the circle in exactly one point, called the point of tangency.
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• Point of tangency- point where tangent intersects a circle
TPoint T is the point of tangency
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Exampletell whether the segment is best described as a chord, secant,
tangent, diameter or radius• Segment AH
• Segment EI
• Segment DF
• Segment CE
A
B
C
D
E
F
G
H
I
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Exampletell whether the segment is best described as a chord, secant,
tangent, diameter or radius• Segment AH
• Segment EI
• Segment DF
• Segment CE
A
B
C
D
E
F
G
H
I
tangentDiameter
Chord
radius
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Tangent circles- circles that intersect in one point
Concentric circles- circles that have a common center but different radii lengths
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Common internal tangent- a tangent that intersects the segment that connects the centers of the circles
Common external tangent- does not intersect the segment that connects the centers
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ExampleCommon internal or external
tangent?
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ExampleCommon internal or external
tangent?
external
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Theorem 14-4• In a plane, a line is tangent to a circle if
and only if it is perpendicular to a radius of the circle at its endpoint on the circle.
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ExampleIs segment CE tangent to circle D?
Explain
D
E
C
11
45
43
Remember in order to find if a line is tangent we need to
know if there is a 90 degree angle
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ExampleIs segment CE tangent to circle D?
Explain
D
E
C
11
45
43
112+432=452
121+1849=20251970=2050
NO
Let’s use the Pythagorean
Theorem
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Examplesolve for the radius, r
A
B
Cr
r28ft
14ft
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Examplesolve for the radius, r
A
B
Cr
r28ft
14ft
r2+282=(r+14)2
r2+ 784=r2+ 28r+196784=28r+196
588=28r21=r
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Theorem 14-6
• Tangent segments from a common external point are congruent.
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Examplesegment AB is tangent to circle C at pt B. segment AD is tangent to
circle C at pt D. Find the value of X
C
B
D
A
x2+8
44
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Examplesegment AB is tangent to circle C at pt B. segment AD is tangent to
circle C at pt D. Find the value of X
C
B
D
A
x2+8
44
x2+8=44x2=36
X=6