Download Geometry Chapter 11 Review

11-1 Lines That Intersect Circles
11-1 Lines That Intersect Circles
Example: Identifying Tangents of Circles
Example: Identifying Lines and Segments That Intersect Circles
1. Identify each line or segment that intersects !P.
2. Identify the point of tangency and write the equation of
the tangent line at this point.
chords:
secant:
tangent:
diameter:
radii:
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Holt Geometry
11-1 Lines That Intersect Circles
11-1 Lines That Intersect Circles
Example: Using Properties of Tangents
4. RS and RT are tangent to !Q. Find RS.
Example: Using Properties of Tangents
5. In each diagram, AB and AC are tangent to !O.
Find each measure.
S
6x
R
x2 + 9
Q
b) m∠A
T
B
O
( x + 2 )!
C
( x − 6 )!
A
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Holt Geometry
11-2
11-1 Lines That Intersect Circles
Example: Using Properties of Tangents
Example: Using the Arc Addition Postulate
6. Assume the segments that appear to be tangent are
tangent. Find CB.
B
C
24
7
A
D
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11-2
Arcs and Chords
1. Find each measure.
!
b) mRQT
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Arcs and Chords
11-3
Sector Area and Arc Length
Example: Finding the Area of a Sector
1. Find the area of sector HGJ. Give answers in terms of π
and rounded to the nearest hundredth.
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m∠VTW .
!
a) mQS
Example: Applying Congruent Angles, Arcs, and Chords
6. Find NP.
2. Find
Sector Area and Arc Length
11-3
Sector Area and Arc Length
11-3
Example: Finding the Area of a Segment
4. Find the area of segment LNM to the nearest hundredth.
Step 1 Find the area of sector LNM.
Example: Finding Arc Length
6. Find each arc length FG. Give answers in terms of π and
rounded to the nearest hundredth.
Step 2 Find the area of ∆LNM.
Step 3 Area of segment LNM
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11-4
Inscribed Angles
Example: Finding Measures of Arcs and Inscribed Angles
2. Find each measure.
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11-4
Example: Finding Angle Measures in Inscribed Triangles
3. Find a.
a)
b) m∠DAE
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Inscribed Angles
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4. Find m∠LJM.
11-4
11-5 Angle Relationships in Circles
Inscribed Angles
Check It Out!
5. Find m∠EDF.
6. Find the angle
measures of GHJK.
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Example: Using Tangent-Secant and Tangent-Chord Angles
1. Find each measure.
a) m∠EFH
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11-5 Angle Relationships in Circles
11-5 Angle Relationships in Circles
Example: Finding Measures Using Tangents and Secants
Example: Finding Angle Measures Inside a Circle
4. Find m∠RNM.
5. Find the value of x.
Text
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b)
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6. Find the value of x.
11-6 Segment Relationships in Circles
Example: Applying the Chord-Chord Product Theorem
1. Find the value of x and the length of each chord.
11-6 Segment Relationships in Circles
Example: Applying the Secant-Secant Product Theorem
3. Find the value of x and the length of each secant
segment.
J
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11-6 Segment Relationships in Circles
Example: Applying the Secant-Secant Product Theorem
4. Find the value of z and the length of each secant
segment.
5. Find the value of x.
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Holt Geometry