1. 11-5: Angle Relationships in Circles
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11-5: Angle Relationships in Circles

2. 11-5: Angle Relationships in Circles
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11-5: Angle Relationships in Circles

3. 11-5: Angle Relationships in Circles
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11-5: Angle Relationships in Circles

4. Page 787
Page 787
23-30 all, 39, 40
16)
56°
17)
90°
18)
124°
19)
260°
20)
64.5°
21)
107.5°
22)
135°
23)
57.5°
24)
40°
25)
18°
26)
66°
27)
45°
28)
117°
29)
90°
30)
100°
39)
115°, 30°, 35°
40)
97°, 32°, 51°
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11-3: Area of a Segment

5. Segment Relationships in Circles
Section 11-5
Geometry PreAP, Revised ©2014
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11-5: Angle Relationships in Circles

6. 11-5: Angle Relationships in Circles
Theorem 1
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11-5: Angle Relationships in Circles

7. 11-5: Angle Relationships in Circles
Example 1
Solve for x and length of each chord
EJ  JF = GJ  JH J
10(7) = 14(x)
70 = 14x
5 = x
EF = = 17
GH = = 19
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11-5: Angle Relationships in Circles

8. 11-5: Angle Relationships in Circles
Example 2
Solve for x and length of each chord
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11-5: Angle Relationships in Circles

9. 11-5: Angle Relationships in Circles
Your Turn
Solve for d and length of each chord
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11-5: Angle Relationships in Circles

10. 11-5: Angle Relationships in Circles
Theorem 2
(Whole)(Outside)
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11-5: Angle Relationships in Circles

11. 11-5: Angle Relationships in Circles
Example 3
Solve for x and the length of each secant segment
16(7) = (8 + x)(8)
112 = x
48 = 8x
6 = x
ED = = 16
EG = = 14
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11-5: Angle Relationships in Circles

12. 11-5: Angle Relationships in Circles
Example 4
Solve for z and the length of each secant segment
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11-5: Angle Relationships in Circles

13. 11-5: Angle Relationships in Circles
Your Turn
Solve for x and the length of each secant segment
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11-5: Angle Relationships in Circles

14. 11-5: Angle Relationships in Circles
Theorem 3
(Whole) (Outside) of Secant = Square the Tangent
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11-5: Angle Relationships in Circles

15. 11-5: Angle Relationships in Circles
Theorem 3
(Whole) (Outside) of Secant = Square the Tangent
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11-5: Angle Relationships in Circles

16. 11-5: Angle Relationships in Circles
Example 5
Solve for x
ML  JL = KL2
20(5) = x2
100 = x2
±10 = x
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11-5: Angle Relationships in Circles

17. 11-5: Angle Relationships in Circles
Example 6
Solve for 𝒚
DE  DF = DG2
7(7 + y) = 102
49 + 7y = 100
7y = 51
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11-5: Angle Relationships in Circles

18. 11-5: Angle Relationships in Circles
Your Turn
Solve for 𝒂
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11-5: Angle Relationships in Circles

19. 11-5: Angle Relationships in Circles
Recap
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11-5: Angle Relationships in Circles

20. 11-5: Angle Relationships in Circles
Recap
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11-5: Angle Relationships in Circles

21. 11-5: Angle Relationships in Circles
Extra Example 1
Find arc RST.
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11-5: Angle Relationships in Circles

22. 11-5: Angle Relationships in Circles
Extra Example 2
Solve for 𝒙
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11-5: Angle Relationships in Circles

23. 11-5: Angle Relationships in Circles
Extra Example 3
Solve for x
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11-5: Angle Relationships in Circles

24. 11-5: Angle Relationships in Circles
Extra Example 4
Solve for x
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11-5: Angle Relationships in Circles

25. 11-5: Angle Relationships in Circles
Extra Example 5
Solve for x
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11-5: Angle Relationships in Circles

26. 11-5: Angle Relationships in Circles
Assignment
Page all, all, 25
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11-5: Angle Relationships in Circles