1. Warm-up A
1. Let AM = 8, BP = 7, and CA = 18. Find the perimeter of the triangle. N M 50 C P
3. MCY = 270 Find BC. B
2. Find ACB 20 B A M
312 20 90 B 24 C C Y

2. 6.5 Other Angle Relationships – On, Inside, and Outside of the Circle

3. Case I: Vertex is ON the circle
ANGLE
ARC
ARC
ANGLE

4. REMEMBER: Find m1. A B 1
124° C
m1 = 62º

5. Ex. 1: Find m1. 1
78°
m1 = 39º

6. 108°
Ex. 2: Find m1. 1
m1 = 126º

7. Case II: Vertex is inside the circle
ARC B
ANGLE D
ARC C
Looks like a PLUS sign!

8. Ex. 4 Find m1.
93° A B 1 D C
113°
m1 = 103º

9. Ex. 5 Find mQT. N Q
84º
92º M T
mQT = 100º

10. Case III: Vertex is outside the circle
ANGLE
small ARC A
LARGE ARC D B
LARGE ARC
LARGE ARC
small ARC
ANGLE
small ARC
ANGLE

11. Ex. 6 Find m1. 1
15° A D
65° B
m1 = 25º

12. Ex. 7 Find mAB. A
27°
70° B
mAB = 16º

13. Ex. 8 Find m1.
260° 1
m1 = 80º

14. 52.5º 4
Brain Buster
32º 2 3
105º
36.5º 1
105º
16º