1. Over Lesson 10–5 5-Minute Check 1 A.yes B.no Determine whether BC is tangent to the given circle. ___ A.A B.B

2. Over Lesson 10–5 5-Minute Check 2 A.yes B.no Determine whether QR is tangent to the given circle. ___ A.A B.B

3. Over Lesson 10–5 A.A B.B C.C D.D 5-Minute Check 3 12 Find x. Assume that segments that appear to be tangent are tangent.

4. Over Lesson 10–5 A.A B.B C.C D.D 5-Minute Check 4 Find x. Assume that segments that appear to be tangent are tangent.

5. Over Lesson 10–5 A.A B.B C.C D.D 5-Minute Check 5 SL and SK are tangent to the circle. Find x. ___ 5

6. Then/Now Find measures of angles formed by lines intersecting on or inside a circle. Find measures of angles formed by lines intersecting outside the circle.

7. Vocabulary secant—A line that intersects a circle in two points.

8. Concept

10. Example 1 Use Intersecting Chords or Secants A. Find x. Theorem 10.12 Substitution Simplify. Answer: x = 82

11. Example 1 Use Intersecting Chords or Secants B. Find x. Theorem 10.12 Substitution Simplify. Step 1Find m  VZW.

12. Example 1 Use Intersecting Chords or Secants Step 2Find m  WZX.  WZX =180 –  VZWDefinition of supplementary angles x =180 – 79Substitution x =101Simplify. Answer: x = 101

13. C. Find x. Theorem 10.12 Substitution Multiply each side by 2. Example 1 Use Intersecting Chords or Secants Subtract 25 from each side. Answer: x = 95

14. A.A B.B C.C D.D Example 1 98 A. Find x.

15. A.A B.B C.C D.D Example 1 95 B. Find x.

16. A.A B.B C.C D.D Example 1 104 C. Find x.

17. Concept

18. Example 2 Use Intersecting Secants and Tangents A. Find m  QPS. Theorem 10.13 Substitute and simplify. Answer: m  QPS = 125

19. B. Theorem 10.13 Example 2 Use Intersecting Secants and Tangents Substitution Multiply each side by 2. Answer:

20. A.A B.B C.C D.D Example 2 112.5 A. Find m  FGI.

21. A.A B.B C.C D.D Example 2 162 B.

22. Concept

23. Example 3 Use Tangents and Secants that Intersect Outside a Circle A. Theorem 10.14 Substitution Multiply each side by 2.

24. Example 3 Use Tangents and Secants that Intersect Outside a Circle Subtract 141 from each side. Multiply each side by –1.

25. Example 3 Use Tangents and Secants that Intersect Outside a Circle B. Theorem 10.14 Substitution Multiply each side by 2.

26. Example 3 Use Tangents and Secants that Intersect Outside a Circle Add 140 to each side.

27. A.A B.B C.C D.D Example 3 23 A.

28. A.A B.B C.C D.D Example 3 230 B.

29. Example 4 Apply Properties of Intersecting Secants Theorem 10.14 Substitution

30. Example 4 Apply Properties of Intersecting Secants Multiply each side by 2. Subtract 96 from each side. Multiply each side by –1.

31. A.A B.B C.C D.D Example 4 40

32. Concept