Transcript Geo Ch 10-7 – Special Segments in a Circle

Special Segments in a Circle
Chapter 10.7
• Find measures of segments that intersect in the
interior of a circle.
• Find measures of segments that intersect in the
exterior of a circle.
Standard 7.0 Students prove and use theorems
involving the properties of parallel lines cut by a
transversal, the properties of quadrilaterals, and the
properties of circles. (Key)
Standard 21.0 Students prove and solve problems
regarding relationships among chords, secants,
tangents, inscribed angles, and inscribed and
circumscribed polygons of circles. (Key)
Chord Segment Theorem
• If two chords intersect in the interior of a circle, then the product of
the lengths of the segments of one chord is equal to the product of
the lengths of the segments of the other chord.
• Forget the words, copy the picture.
E
A
5 cm
2 cm
B
4 cm D
10 cm
C
(AB)(BC) = (DB)(BE)
(2)(10) = (4)(5)
20 = 20
Intersection of Two Chords
Find x.
Answer: 13.5
Find x.
A. 14
B. 12.5
C. 2
D. 18
0%
0%
A
B
A. A
B. 0% B
C. C
C
D. D
0%
D
Example: Solve for x
E
A
x + 2 cm
3 cm
B
6 cm
3x - 1 cm
C
D
6(x + 2) = 3(3x – 1)
6x + 12 = 9x – 3
15 = 3x
5=x
BIOLOGY Biologists often examine organisms
under microscopes. The circle represents the field
of view under the microscope with a diameter of 2
mm. Determine the length of the organism if it is
located 0.25 mm from the bottom of the field of
view. Round to the nearest hundredth.
1.75
x  .4375
x
x
ARCHITECTURE Phil is installing a new window in
an addition for a client’s home. The window is a
rectangle with an arched top called an eyebrow. The
diagram below shows the dimensions of the
window. What is the radius of the circle containing
the arc if the eyebrow portion of the window is not a
semicircle?
Hint:
A. 10 ft
B. 20 ft
C. 36 ft
D. 18 ft
1.
2.
3.
4.
A
B
C
D
0%
A
B
C
D
Secant Segment Theorem
• If two secant segments share the same endpoint outside a circle,
then the product of the length of one secant segment and the
length of its external segment equals the product of the length of
the other secant segment and the length of its external segment.
• Forget the words, copy the picture.
C
B
A
D
E
(AB)(AC) = (AD)(AE)
Example: Solve for x
(9)(20) = (10)(10 + x)
180 = 100 + 10x
80 = 10x
C
8=x
20
A
11
B
9
10
D
x
E
10 + x
Intersection of Two Secants
Find x if EF = 10, EH = 8, and FG = 24.
Answer: 34.5
Find x if GO = 27, OM = 25, and IK = 24.
A. 28.125
0%
B. 50
C. 26
D. 28
1.
2.
3.
4.
A
A
B
C
D
B
C
D
Secant-Tangent Segment Theorem
• If a secant segment and a tangent segment share an endpoint
outside a circle, then the product of the length of the secant
segment and the length of its external segment equals the square
of the length of the tangent segment.
• Forget the words, copy the picture.
B
(AC)(AD) = (AB)2
A
C
D
Example: Solve for x
12
B
A
6
(6)(6 + x) = (12)2
36 + 6x = 144
6x = 108
x = 18
C
x
6+x
D
Intersection of a Secant and a Tangent
Find x. Assume that segments that appear to be
tangent are tangent.
Answer: 8
Disregard the negative solution.
Find x. Assume that segments that appear to be
tangent are tangent.
A. 22.36
B. 25
C. 28
0%
0%
A
B
D. 30
A. A
B. 0% B
C. C
C
D. D
0%
D
Homework
Chapter 10.7
• Pg 611
5 – 15,
17 – 24,
41 – 43