1. CIRCLES AND ANGLES Section 10-4, 10-6 spi.3.3.A, spi.3.3.B
Jim Smith JCHS

2. Central Angles 1 = 63° 63° Central Angles Are Equal To The
Measure Of The Intercepted Arc
63°
1 = 63° 1

3. The Vertex Of Inscribed Angles Are On The Circle And The Sides Are
Contained In Chords. 2 4 3 1

4. The Measure Of An Inscribed Angle Is Equal To ½ The Measure Of The
Intercepted Arc 1 2 4 3
2 = ½ (180 )
2 = 90°
1 = ½ ( 100 )
1 = 50°
100°

5. Any Angle With It’s Vertex
On The Circle Is Equal
To ½ Of The Arc.
A secant and
a tangent
2 secants

6. ½ The Sum Of The Arcs If The Vertex Is Somewhere
Inside The Circle But Not At The
Center, The Angle Is Equal To
½ The Sum Of The Arcs
150°
8 = ½ ( )
8 = ½ ( 230 )
8 = 115° 8
80°

7. ½ The Difference Of The Arcs.
If The Vertex Is Outside
(A Distance Away From) The
Circle, The Arc Is Equal To
½ The Difference Of The Arcs. 5
50°
5 = ½ ( )
5 = ½ ( 70 )
5 = 35°
120°

8. = arc =1/2 arc 1 4 3 =1/2 (difference =1/2 (sum of of 2 arcs) 2 arcs)

9. D A C F E B AF is a tangent AC is a diameter CD = 100° CB = AE
BE = 50° D A 1 2 4 C
Find the
Measures of
the angles 5 F 3 E B

10. D A C F E B 50° AF is a tangent AC is a diameter CD = 100° 80° CB = AE
BE = 50° D
80°
100° A 1 2 4
65° C 5 F
130/2 =65 3 E
65° B
50°

11. D
80°
1 = 80°
100° A 1 2 4
65° C 5 F 3 E
65° B
50°

12. D
80°
2 =1/2 (65)
2 = 32 ½ °
100° A 1 2 4
65° C 5 F 3 E
65° B
50°

13. D A F C E B 50° 80° 100° 3 =1/2 (180+50) 3 =1/2 (230) 3 = 115° 65° 65°4
65° F C 5 3 E
65° B
50°

14. D A C F E B 50° 4 =1/2 (65+50) 80° 4 =1/2 (115) 100° 4 = 57 ½ ° 65°3 E
65° B
50°

15. D A C F E B 50° 5 =1/2 (180-65) 80° 5 =1/2 (115) 100° 5 =57 1/2° 65°4
65° C 5 F 3 E
65° B
50°