1. Warm up 30  80  100  180  100  260 

2. Inscribed Angles and Inscribed Quadrilaterals

3. Central Angle Central Angle = Arc

4. Inscribed Angle Angle where the vertex is ON the circle

5. Inscribed Angle Inscribed Angle = intercepted Arc/2

6. 160  80  The arc is twice as big as the angle!!

7. Inscribed angles

8. 120  x y Find the value of x and y.    = 120  = 60 

9. Examples 1. If m JK = 80  and  JMK = 2x – 4, find x. M Q K S J 2. If m  MKS = 56 , find m MS. x = 22 112 

10. If two inscribed angles intercept the same arc, then they are congruent.  BAD =  BCD A B C D

11. Find the measure of  DOG,  DIG,  ODI and  OGI D O G I 102 74

12. If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

13. Quadrilateral inscribed in a circle: opposite angles are SUPPLEMENTARY A B C D

14. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle. diameter

15. Example 3 In  J, m  3 = 5x and m  4 = 2x + 9. Find the value of x. 3 Q D J T U 4 5x = 2x + 9 x = 3 3x = + 9

16. 4x – 14 = 90 H K G N Example 4 In  K, GH is a diameter and m  GNH = 4x – 14. Find the value of x. x = 26 4x = 104

17. z 2x + 18 85 2x +18 + 22x – 6 = 180 x = 7 z + 85 = 180 z = 95 Example 5 Solve for x and z. 22x – 6 24x +12 = 180 24x = 168

18. Textbook p. 420 #2 – 13 (omit #6), 17 – 20, 22