Download - Lesson 6.1 Properties of Tangents
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Lesson 6.1 Properties of Tangents
Page 182
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Q1 Select A
A.) This is the correct answer.
B.) This is the wrong answer.
C.) This is just as wrong as B
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Q2 This time select B
A.) This is the wrong choice.
B.) This is the correct choice.
C.) Do not select this answer.
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Circle
• A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.
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Radius
• A radius is a segment whose endpoints are the center and any point on the circle.
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Chord
• A chord is a segment whose endpoints are on a circle.
What is special about this one?
• A diameter is a chord that contains the center of the circle.
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Secant Tangent• A secant is a line that intersects a circle in two
points.• A tangent is a line in the plane of a circle that
intersects the circle in exactly one point, the point of tangency.
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Q3 Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of
circle P.A.) radius
B.) chord
C.) diameter
D.) secant
E.) tangent
RT
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Q4 Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of
circle P.A.) radius
B.) chord
C.) diameter
D.) secant
E.) tangent
WT��������������
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Q5 Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of
circle P.A.) radius
B.) chord
C.) diameter
D.) secant
E.) tangent
PT
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Q6 Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of
circle P.A.) radius
B.) chord
C.) diameter
D.) secant
E.) tangent
RQ�������������� �
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Q7 How many common tangents are possible between the two circles?
A.) 1
B.) 2
C.) 3
D.) 4
E.) 5
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Q8 How many common tangents are possible between the two circles?
A.) 1
B.) 2
C.) 3
D.) 4
E.) 5
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Q9 How many common tangents are possible between the two circles?
A.) 1
B.) 2
C.) 3
D.) 4
E.) 5
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Theorem 6.1:
• In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle.
mABC = 90.00
C
B
A
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Theorem 6.2:
• Tangent segments from a common external point are congruent.
mDEC = 90.00mABC = 90.00
DC
B
A
E
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222 cba
If we show that angle ABC is 90⁰ then segment BC must be a tangent.
222 1068 1003664
100100 So angle ABC is 90⁰ and the segment BC is perpendicular to radius AB.
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Example 5
222 cba 222 )50(70 rr
25001004900 22 rrr25002500 22 rr
r1002400 100100r24
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Q10 What is the value of r?
A.) 1 cm
B.) 2 cm
C.) 3 cm
D.) 4 cm
E.) 5 cm
mDCB = 90
r
r
BC = 4 cm
AB = 2 cm
A
C
D
B
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Homework1-22 page 186
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Use the diagram to determine if the statement is true or false.
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222 cba 222 )36(48 rr
________________ 22 rrr
Hint
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222 cba 222 )1804000(4000 d
Hint