1. Splash Screen

2. CCSS Content Standards Reinforcement of G.C.4 Construct a tangent line from a point outside a given circle to the circle. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 1 Make sense of problems and persevere in solving them.

3. Then/Now You found measures of segments formed by tangents to a circle. Find measures of angles formed by lines intersecting on or inside a circle. Find measures of angles formed by lines intersecting outside the circle.

4. Vocabulary secant A Secant is a line that intersects a circle in exactly 2 points

5. Concept

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

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

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

9. 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

10. Example 1 A.92 B.95 C.98 D.104 A. Find x.

11. Example 1 A.92 B.95 C.97 D.102 B. Find x.

12. Example 1 A.96 B.99 C.101 D.104 C. Find x.

13. Concept

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

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

16. Example 2 A.98 B.108 C.112.5 D.118.5 A. Find m  FGI.

17. Example 2 A.99 B.148.5 C.162 D.198 B.

18. Concept

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

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

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

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

23. Example 3 A.23 B.26 C.29 D.32 A.

24. Example 3 A.194 B.202 C.210 D.230 B.

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

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

27. Example 4 A.25 B.35 C.40 D.45

28. Concept

29. End of the Lesson