find the lengths of segments formed by lines that intersect circles
DESCRIPTION
Objectives. Find the lengths of segments formed by lines that intersect circles. Use the lengths of segments in circles to solve problems. J. Example 1: Applying the Chord-Chord Product Theorem. Find the value of x. 10(7) = 14 ( x ). 70 = 14 x. 5 = x. EF = 10 + 7 = 17. - PowerPoint PPT PresentationTRANSCRIPT
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Holt McDougal Geometry
11-6Segment Relationships in Circles
Find the lengths of segments formed by lines that intersect circles.
Use the lengths of segments in circles to solve problems.
Objectives
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Holt McDougal Geometry
11-6Segment Relationships in Circles
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Holt McDougal Geometry
11-6Segment Relationships in Circles
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Holt McDougal Geometry
11-6Segment Relationships in Circles
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Holt McDougal Geometry
11-6Segment Relationships in Circles
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Holt McDougal Geometry
11-6Segment Relationships in Circles
Example 1: Applying the Chord-Chord Product Theorem
Find the value of x.
EJ JF = GJ JH
10(7) = 14(x)
70 = 14x
5 = x
EF = 10 + 7 = 17
GH = 14 + 5 = 19
J
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Holt McDougal Geometry
11-6Segment Relationships in Circles
Check It Out! Example 1
Find the value of x and the length of each chord.
DE EC = AE EB
8(x) = 6(5)
8x = 30
x = 3.75
AB = 6 + 5 = 11
CD = 3.75 + 8 = 11.75
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Holt McDougal Geometry
11-6Segment Relationships in Circles
Check It Out! Example 2
Suppose the length of chord AB that the archeologists measured was 12 in. Find QR.
AQ QB = PQ QR
6(6) = 3(QR)
12 = QR
12 + 3 = 15 = PR
6 in.
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Holt McDougal Geometry
11-6Segment Relationships in Circles
Find the value of x and the length of each secant segment.
Example 3: Applying the Secant-Secant Product Theorem
16(7) = (8 + x)8
112 = 64 + 8x
48 = 8x
6 = x
ED = 7 + 9 = 16
EG = 8 + 6 = 14
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Holt McDougal Geometry
11-6Segment Relationships in Circles
Check It Out! Example 3
Find the value of z and the length of each secant segment.
39(9) = (13 + z)13
351 = 169 + 13z
182 = 13z
14 = z
LG = 30 + 9 = 39
JG = 14 + 13 = 27
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Holt McDougal Geometry
11-6Segment Relationships in Circles
Example 4: Applying the Secant-Tangent Product Theorem
Find the value of x.
The value of x must be 10 since it represents a length.
ML JL = KL2
20(5) = x2
100 = x2
±10 = x
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Holt McDougal Geometry
11-6Segment Relationships in Circles
Check It Out! Example 4
Find the value of y.
DE DF = DG2
7(7 + y) = 102
49 + 7y = 100
7y = 51