4. 7.7 What More Can I Learn About Circles? Pg. 24 Angles Inside and Outside Circles

5. 7.7 – What More Can I Learn About Circles? Inside and Outside Circles So far you have investigated when an angle is formed at the center or the side of the circle. Today you are going to continue to find angle measures that are inside and outside of circles.

6. 7.35 –ANGLE LOCATION Determine if the angle formed is inside, outside, at the center, or on the circle.. on centerinsideoutside

7. 7.36 – INSIDE ANGLES Uri now has a challenge for you: What happens when chords intersect inside a circle? Discover the relationship between the inside angle and the two intercepting arcs.

8. ½a ½b 180-½a-½b ½a + ½b x = a + b 2 x = arc + arc 2

9. If an angle is formed inside of a circle not at the center, then the angle is ________ the ___________ of the two intercepted arcs. half sum vertical Inside angle = arc + arc 2

10. 7.37 – EXTRA PRACTICE Using the information you have learned, find the missing variables. x°

11. x = 86 + 88 2 x = 174 2

12. x = 120 + 98 2 x = 218 2

13. 7.38 – OUTSIDE ANGLES Uri now has a new challenge for you: What happens when secants and tangents intersect outside a circle?

14. ab ½ b ½ a 180 – ½b x°x° x + ½ a + 180 – ½ b = 180 x + ½ a – ½ b = 0 x = ½ b – ½ a x = b – a 2 x = Big arc – little arc 2

15. b ax http://www.cpm.org/flash/tech nology/sectangent.swf

16. If an angle is formed outside of a circle, then the angle is ________ the ________________ of the two intercepted arcs. half difference Outside angle = big arc – little arc 2

17. 7.39 – EXTRA PRACTICE Using the information you have learned, find the missing variables. x ° y ° x °

18. x = B – L 2 x = 90 – 20 2 x = 70 2 x = 35°

19. 41 ° y = B – L 2 y = 111 – 41 2 y = 70 2 y = 35°

20. 56 ° B – L 2 134 – 56 2 78 2 39°

21. 117 ° x = B – L 2 x = 243 – 117 2 x = 126 2 x = 63°