1. Secants, Tangents and Angle Measures
Chapter 10-6

2. Find measures of angles formed by lines intersecting on or inside a circle.
secant
Find measures of angles formed by lines intersecting outside the circle.
Standard Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. (Key)
Standard Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. (Key)
Lesson 6 MI/Vocab

3. Tangent-Chord (or secant) Theorem
If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half its intercepted arc
100o X Y
mX = ½ (100o)
mX = 50o
mY = ½ (260o)
mY = 130o

4. Secant-Tangent Angle
110o
Answer: 55
Lesson 6 Ex2

5. A. 122
B. 58
C. 106
D. 116 A B C D
Lesson 6 CYP2

6. 2-Chord (or Secant) Theorem
If 2 chords intersect in the interior of a circle, then the measure of the angle formed is one half of the sum of the arcs intercepted by the angle and its vertical angle.
100o X
40o
mX = ½ ( )
mX = ½ (140)
mX = 70o

7. Secant-Secant Angle
Method 1
Lesson 6 Ex1

8. Secant-Secant Angle
Method 2
Answer: 98
Lesson 6 Ex1

9. A. 42
B. 84
C. 96
D. 138 A B C D
Lesson 6 CYP1

10. 2-Line Theorem
If 2 lines intersect on the exterior of a circle, then the measure of the angle formed is one half of the difference of the 2 intercepted arcs.

11. Example:
100o X
40o
mX = ½ ( )
mX = ½ (60)
mX = 30o

12. Secant-Secant Angle
Find x.
Answer: 17
Lesson 6 Ex3

13. Find x.
A. 76
B. 73
C. 111
D. 146 A B C D
Lesson 6 CYP3

14. JEWELRY A jeweler wants to craft a pendant with the shape shown
JEWELRY A jeweler wants to craft a pendant with the shape shown. Use the figure to determine the measure of the arc at the bottom of the pendant.
360 – x
Answer: 220 x
Lesson 6 Ex4

15. PARKS Two sides of a fence to be built around a circular garden in a park are shown. Use the figure to determine the measure of A.
A. 75 B
C. 105
D. 52.5 A B C D
Lesson 6 CYP4

16. Secant-Tangent Angle
Find x.
141°
62° x°
62 = (141 – x)
124 = 141 – x
–17 = –x
17 = x
Answer: x = 17
Lesson 6 Ex5

17. Find x. A.
B. 5
C. 9 D. A B C D
Lesson 6 CYP5

18. Homework
Chapter 10.6
Pg 603
6 – 26,
32 – 34,
55 – 57