1. Splash Screen

2. Example 1: Use Intersecting Chords or Secants Theorem 10.13
CCSS
Then/Now
New Vocabulary
Theorem 10.12
Example 1: Use Intersecting Chords or Secants
Theorem 10.13
Example 2: Use Intersecting Secants and Tangents
Theorem 10.14
Example 3: Use Tangents and Secants that Intersect Outside a Circle
Example 4: Real-World Example: Apply Properties of Intersecting Secants
Concept Summary: Circle and Angle Relationships
Lesson Menu

3. Mathematical Practices
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.
CCSS

4. 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.
Then/Now

5. A secant contains a chord.
Secant – a line that cuts through a circle and intersects the circle in two points
A secant contains a chord.
Vocabulary

6. Concept

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

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

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

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

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

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

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

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

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

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

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

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

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

20. Concept

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

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

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

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

25. A. Find mFGI.
A. 98
B. 108 C D
Example 2

26. A. Find mFGI.
A. 98
B. 108 C D
Example 2

27. B.
A. 99 B
C. 162
D. 198
Example 2

28. B.
A. 99 B
C. 162
D. 198
Example 2

29. Concept

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

45. Concept

46. End of the Lesson