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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 Presentation
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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
Holt McDougal Geometry
11-6Segment Relationships in Circles
Holt McDougal Geometry
11-6Segment Relationships in Circles
Holt McDougal Geometry
11-6Segment Relationships in Circles
Holt McDougal Geometry
11-6Segment Relationships in Circles
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
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
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.
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
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
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
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