Transcript Slide 1

11-6
11-6Segment
SegmentRelationships
RelationshipsininCircles
Circles
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Geometry
Holt
Geometry
11-6 Segment Relationships in Circles
Warm Up
Solve for x.
1.
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2. 3x = 122 48
3. BC and DC are tangent
to A. Find BC.
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Holt Geometry
11-6 Segment Relationships in Circles
Objectives
Find the lengths of segments formed by
lines that intersect circles.
Use the lengths of segments in circles
to solve problems.
Holt Geometry
11-6 Segment Relationships in Circles
Vocabulary
secant segment
external secant segment
tangent segment
Holt Geometry
11-6 Segment Relationships in Circles
In 1901, divers near the Greek island of
Antikythera discovered several fragments
of ancient items. Using the mathematics of
circles, scientists were able to calculate the
diameters of the complete disks.
The following theorem describes the
relationship among the four segments that
are formed when two chords intersect in
the interior of a circle.
Holt Geometry
11-6 Segment Relationships in Circles
Holt Geometry
11-6 Segment Relationships in Circles
Example 1: Applying the Chord-Chord Product
Theorem
Find the value of x and the length of each chord.
EJ  JF = GJ  JH
10(7) = 14(x)
70 = 14x
5=x
EF = 10 + 7 = 17
GH = 14 + 5 = 19
Holt Geometry
J
11-6 Segment 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 Geometry
11-6 Segment Relationships in Circles
Example 2: Art Application
The art department is
contracted to construct a
wooden moon for a play. One
of the artists creates a
sketch of what it needs to
look like by drawing a chord
and its perpendicular
bisector. Find the diameter
of the circle used to draw the
outer edge of the moon.
Holt Geometry
11-6 Segment Relationships in Circles
Example 2 Continued
8  (d – 8) = 9  9
8d – 64 = 81
8d = 145
Holt Geometry
11-6 Segment Relationships in Circles
Check It Out! Example 2
What if…? Suppose the length of chord AB
that the archeologists drew was 12 in. In this
case how much longer is the disk’s diameter
compared to the disk on p. 793?
AQ  QB = PQ  QR
6(6) = 3(QR)
12 = QR
12 + 3 = 15 = PR
Holt Geometry
6 in.
11-6 Segment Relationships in Circles
A secant segment is a segment of a secant with at
least one endpoint on the circle. An external secant
segment is a secant segment that lies in the exterior
of the circle with one endpoint on the circle.
Holt Geometry
11-6 Segment Relationships in Circles
Holt Geometry
11-6 Segment Relationships in Circles
Example 3: Applying the Secant-Secant Product
Theorem
Find the value of x and the length of each
secant segment.
16(7) = (8 + x)8
112 = 64 + 8x
48 = 8x
6=x
ED = 7 + 9 = 16
EG = 8 + 6 = 14
Holt Geometry
11-6 Segment 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 Geometry
11-6 Segment Relationships in Circles
A tangent segment is a segment of a tangent
with one endpoint on the circle. AB and AC are
tangent segments.
Holt Geometry
11-6 Segment Relationships in Circles
Holt Geometry
11-6 Segment Relationships in Circles
Example 4: Applying the Secant-Tangent Product
Theorem
Find the value of x.
ML  JL = KL2
20(5) = x2
100 = x2
±10 = x
The value of x must be 10 since it represents a
length.
Holt Geometry
11-6 Segment 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
Holt Geometry
11-6 Segment Relationships in Circles
Lesson Quiz: Part I
1. Find the value of d and the
length of each chord.
d=9
ZV = 17
WY = 18
2. Find the diameter of the plate.
Holt Geometry
11-6 Segment Relationships in Circles
Lesson Quiz: Part II
3. Find the value of x and the
length of each secant segment.
x = 10
QP = 8
QR = 12
4. Find the value of a.
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Holt Geometry