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

2. Review HW

3. Inscribed Angles and Inscribed Quadrilaterals

4. Wheel of Formulas!!

5. Central Angle
Angle = Arc

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

7. Inscribed Angle

8. 160
The arc is twice as big as the angle!!
80

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

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

11. Find the measure of DOG and DIG
72˚
If two inscribed angles intercept the same arc, then they are congruent. G O I

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

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

15. x = 3 5x = 2x + 9 3x = + 9 In J, m3 = 5x and m 4 = 2x + 9.
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
3x = + 9
x = 3

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

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

18. Secant and Tangent Angles
Vertex is INSIDE OR OUTSIDE the circle

19. Vertex is INSIDE the Circle NOT at the Center

20. Ex. 1 Solve for x
180 – 88 X
88
84 92
x = 100

21. Ex. 2 Solve for x.
360 – 89 – 93 – 45
45
93 xº
89
133
x = 89

22. Vertex is OUTside the Circle

23. Ex. 3 Solve for x. x
15°
x = 25
65°

24. Ex. 4 Solve for x.
27° x
70°
x = 16

25. Ex. 5 Solve for x.
360 – 260
260°
100 x
x = 80

26. Tune: If You’re Happy and You Know It
If the vertex is ON the circle half the arc. <clap, clap>
If the vertex is IN the circle half the sum. <clap, clap>
But if the vertex is OUTside, then you’re in for a ride, cause it’s half of the difference anyway. <clap, clap>