1. WARM UP 1) 2)

2. Section 9.6 Other Angles

3. OTHER Angles in a Circle You know two types of Angles: –Central angles –Inscribed angles FOUR OTHER TYPES 1) Two Chords 2) Two Secants 3) Two Tangents 4) One Secant and One Tangent

4. #1 TWO CHORDS 1)Draw a circle 2)Draw two intersecting chords 3)Label one chord with T and O 4)Label the other chord Y and M 5)Label point where they intersect as K How do you find the measure of an interior angle of a circle? T O M Y K 1

5. Find the m ∠ 1 and m ∠ 2. o o o m ∠ 2 = ½(56 + 97) m ∠ 2 = ½(153) m ∠ 2 = 76.5 o m ∠ 1 = 180 – 76.5 m ∠ 1 = 103.5 o

6. #2 TWO SECANTS 1)Draw a circle 2)Plot point W outside of the circle 3)Draw two secant lines starting at point W going through the circle. 4)Label the intercepting arcs x and y. How do we find the measures of these arcs? W xoxo yoyo 1

7. Find the m ∠ 1. o o m ∠ 1 = ½(92 – 23) m ∠ 1 = ½(69) m ∠ 1 = 34.5 o

8. #3 TWO TANGENTS 1)Draw a circle 2)Plot point J outside of the circle 3)Draw two tangent lines starting at point J 4)Label the intercepting arcs x and y How do we find the measures of these arcs? J xoxo yoyo 2

9. Find the missing measure o o o 78 o = ½(x – 102) 78(2) = x – 102 156 = x – 102 258 = x

10. #4 A SECANT and A TANGENT 1)Draw a circle 2)Plot point F outside of the circle 3)Draw one tangent and one secant from F 4)Label the intercepting arcs x and y. How do we find the measures of these arcs? F xoxo yoyo 3

11. Find the missing measures o o o 37 o = ½(x – 65) 37(2) = x – 65 74 = x – 65 139 o = x

12. Problemas! Page 358-359 Classroom Exercises #1-9 DRAW the DIAGRAMS