Special Segments in a Circle

1
Special Segments in a Circle

• Chapter 10.7

2
Lesson 7 MI/Vocab

• 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)
3
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
(AB)(BC) (DB)(BE) (2)(10) (4)(5) 20 20
B
D
C
4
Lesson 7 Ex1
Intersection of Two Chords
Find x.
Answer 13.5
5
Lesson 7 CYP1
Find x.
A. 14 B. 12.5 C. 2 D. 18

1. A
2. B
3. C
4. D

6
Example Solve for x

• 6(x 2) 3(3x 1)
• 6x 12 9x 3
• 15 3x
• 5 x

7
Lesson 7 Ex2
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
8
Lesson 7 CYP2
ARCHITECTURE Phil is installing a new window in
an addition for a clients 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?

1. A
2. B
3. C
4. D

A. 10 ft B. 20 ft C. 36 ft D. 18 ft
9
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.

(AB)(AC) (AD)(AE)
10
Example Solve for x

• (9)(20) (10)(10 x)
• 180 100 10x
• 80 10x
• 8 x

11
Lesson 7 Ex3
Intersection of Two Secants
Find x if EF 10, EH 8, and FG 24.
Answer 34.5
12
Lesson 7 CYP3
Find x if GO 27, OM 25, and IK 24.
A. 28.125 B. 50 C. 26 D. 28

1. A
2. B
3. C
4. D

13
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.

(AC)(AD) (AB)2
14
Example Solve for x

• (6)(6 x) (12)2
• 36 6x 144
• 6x 108
• x 18

15
Lesson 7 Ex4
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.
16
Lesson 7 CYP4
Find x. Assume that segments that appear to be
tangent are tangent.
A. 22.36 B. 25 C. 28 D. 30

1. A
2. B
3. C
4. D

17
Homework

• Chapter 10.7
• Pg 611
• 5 15,
• 17 24,
• 41 43