1. Warm Up
Solve for x. 1.
2. 3x = 122
3. BC and DC are tangent
to A. Find BC. 4 48 14

2. Main Ideas or questions Summary (Last Page of Notes)
Even
Odd
Through IN
2/18 Segment Relationships in Circles
Segment Relationships in Circles
Objectives: Given a circle, TSW find the lengths of segments formed by lines that intersect circles and use the lengths of segments in circles to solve problems.
Warm Up:
Starter Problems 1-3
Main Ideas or questions
Daily Assignment:
14-5 Practice B (Due 2/17)
Journal Summary (Due 2/17)
11-4 Practice B (Due 2/11)
11-3 Practice B (Due 2/9)
11-1/2 Practice B (Due 2/5)
OUT
Summary (Last Page of Notes)

3. Agenda 11-6 Warmup Problems 11-6 Presentation and Discussion
11-6 Homework Preview

4. Journal Summary (Due 2/16)
Write a page summary of the relationships of circles, tangents, chords, arcs, and angles. Explain how to:
1) construct a tangent line to a circle
2) what the relationships are between the central angle, minor arc, major arc, intercepted arc and corresponding chords
3) what the relationship is between the inscribed angle and intercepted arc
4) similarities and differences between the lines that intersect circles - chords, secants, and tangents 4 4 4 4 4 4 4

5. Objectives
Given a circle, TSW find the lengths of segments formed by lines that intersect circles and use the lengths of segments in circles to solve problems.

6. Vocabulary
secant segment
external secant segment
tangent segment

7. 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.

9. Example 1: Applying the Chord-Chord Product Theorem
Find the value of x and the length of each chord.
EJ  JF = GJ  JH J
10(7) = 14(x)
70 = 14x
5 = x
EF = = 17
GH = = 19

10. 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 = = 11
CD = = 11.75

11. 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.

12. Example 2 Continued
8  (d – 8) = 9  9
8d – 64 = 81
8d = 145

13. A secant segment is a segment of a secant
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.

15. 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 = x
48 = 8x
6 = x
ED = = 16
EG = = 14

16. Check It Out! Example 3
Find the value of z and the length of each secant segment.
39(9) = (13 + z)13
351 = z
182 = 13z
14 = z
LG = = 39
JG = = 27

17. A tangent segment is a segment of a tangent with one endpoint on the circle. AB and AC are tangent segments.

19. 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.

20. Check It Out! Example 4
Find the value of y.
DE  DF = DG2
7(7 + y) = 102
49 + 7y = 100
7y = 51

21. 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.

22. 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. 8