1. external secant segment tangent segment
chord segment
secant segment
external secant segment
tangent segment
Vocabulary

2. Concept

3. A. Find x. AE • EC = BE • ED Theorem 10.15 x • 8 = 9 • 12 Substitution
Use the Intersection of Two Chords
A. Find x.
AE • EC = BE • ED Theorem 10.15
x • 8 = 9 • 12 Substitution
8x = 108 Multiply.
x = 13.5 Divide each side by 8.
Answer: x = 13.5
Example 1

4. x • (x + 10) = (x + 2) • (x + 4) Substitution
Use the Intersection of Two Chords
B. Find x.
PT • TR = QT • TS Theorem 10.15
x • (x + 10) = (x + 2) • (x + 4) Substitution
x2 + 10x = x2 + 6x + 8 Multiply.
10x = 6x + 8 Subtract x2 from each side.
Example 1

5. 4x = 8 Subtract 6x from each side. x = 2 Divide each side by 4.
Use the Intersection of Two Chords
4x = 8 Subtract 6x from each side.
x = 2 Divide each side by 4.
Answer: x = 2
Example 1

6. A. Find x.
A. 12
B. 14
C. 16
D. 18
Example 1

7. B. Find x.
A. 2
B. 4
C. 6
D. 8
Example 1

8. Find Measures of Segments in Circles
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.
Example 2

9. Find Measures of Segments in Circles
Understand Two cords of a circle are shown. You know that the diameter is 2 mm and that the organism is 0.25 mm from the bottom.
Plan Draw a model using a circle. Let x represent the unknown measure of the equal lengths of the chord which is the length of the organism. Use the products of the lengths of the intersecting chords to find the length of the organism.
Example 2

10. Solve The measure of EB = 2.00 – 0.25 or 1.75 mm.
Find Measures of Segments in Circles
Solve The measure of EB = 2.00 – 0.25 or mm.
HB ● BF = EB ● BG Segment products
x ● x = 1.75 ● 0.25 Substitution
x2 = Simplify.
x ≈ 0.66 Take the square root of each side.
Answer: The length of the organism is millimeters.
Example 2

11. Find Measures of Segments in Circles
Check Use the Pythagorean Theorem to check the triangle in the circle formed by the radius, the chord, and part of the diameter.
12 ≈ (0.75)2 + (0.66)2 ?
1 ≈ ?
1 ≈ 1 
Example 2

12. 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?
A. 10 ft
B. 20 ft
C. 36 ft
D. 18 ft
Example 2

13. Concept

14. Use the Intersection of Two Secants
Find x.
Example 3

15. Distributive Property
Use the Intersection of Two Secants
Theorem 10.16
Substitution
Distributive Property
Subtract 64 from each side.
Divide each side by 8.
Answer: 34.5
Example 3

16. Find x. A
B. 50
C. 26
D. 28
Example 3

17. Concept

18. LM is tangent to the circle. Find x. Round to the nearest tenth.
Use the Intersection of a Secant and a Tangent
LM is tangent to the circle. Find x. Round to the nearest tenth.
LM2 = LK ● LJ
122 = x(x + x + 2)
144 = 2x2 + 2x
72 = x2 + x
0 = x2 + x – 72
0 = (x – 8)(x + 9)
x = 8 or x = –9
Answer: Since lengths cannot be negative, the value of x is 8.
Example 4

19. Find x. Assume that segments that appear to be tangent are tangent.
C. 28
D. 30
Example 4