1. Geometry – Arcs, Central Angles, and Chords
An arc is part of a circle. There are three types you need to understand: X P A B
Semicircle – exactly half of a circle
180°

2. Geometry – Arcs, Central Angles, and Chords
An arc is part of a circle. There are three types you need to understand: X C P A B D
Semicircle – exactly half of a circle
180° P
Minor arc – less than a semicircle ( < 180° )

3. Geometry – Arcs, Central Angles, and Chords
An arc is part of a circle. There are three types you need to understand: X C B P A B D
Semicircle – exactly half of a circle
180° P P E A
Minor arc – less than a semicircle ( < 180° )
Major arc – bigger than a semicircle
( > 180° )

4. Geometry – Arcs, Central Angles, and Chords
An arc is part of a circle. There are three types you need to understand: X C B P A B D
Semicircle – exactly half of a circle
180° P P E A
Minor arc – less than a semicircle ( < 180° )
Major arc – bigger than a semicircle
( > 180° )
The symbol for an arc ( ) is placed above the letters naming the arc

5. Geometry – Arcs, Central Angles, and Chords
An arc is part of a circle. There are three types you need to understand: X C B P A B D
Semicircle – exactly half of a circle
180° P P E A
Minor arc – less than a semicircle ( < 180° )
Major arc – bigger than a semicircle
( > 180° )
AXB
You need 3 letters to name a semicircle
The symbol for an arc ( ) is placed above the letters naming the arc

6. Geometry – Arcs, Central Angles, and Chords
An arc is part of a circle. There are three types you need to understand: X C B P CD A B D
Semicircle – exactly half of a circle
180° P P E A
Minor arc – less than a semicircle ( < 180° )
- Use the ray endpoints to name a minor arc
Major arc – bigger than a semicircle
( > 180° )
AXB
You need 3 letters to name a semicircle
The symbol for an arc ( ) is placed above the letters naming the arc

7. Geometry – Arcs, Central Angles, and Chords
An arc is part of a circle. There are three types you need to understand: X C B
BEA P CD A B D
Semicircle – exactly half of a circle
180° P P E A
Minor arc – less than a semicircle ( < 180° )
- Use the ray endpoints to name a minor arc
Major arc – bigger than a semicircle
( > 180° )
- Use the ray endpoints and a point in between to name a major arc
AXB
You need 3 letters to name a semicircle
The symbol for an arc ( ) is placed above the letters naming the arc

8. Geometry – Arcs, Central Angles, and Chords
A central angle is an angle whose vertex is at the center of a circle: D C P

9. Geometry – Arcs, Central Angles, and Chords
A central angle is an angle whose vertex is at the center of a circle: D CD C P
- This central angle creates an arc that is equal to the measure of the central angle.

10. Geometry – Arcs, Central Angles, and Chords
A central angle is an angle whose vertex is at the center of a circle: D CD C P
The reverse is also true, if arc CD = 50°, central angle DPC = 50°
This central angle creates an arc that is equal to the measure of the central angle

11. Geometry – Arcs, Central Angles, and ChordsP Y
Chord DC separates circle P into two arcs, minor arc DC, and major arc DYC.

12. Geometry – Arcs, Central Angles, and ChordsP A B
Theorem : if two chords of a circle have the same length, their intercepted arcs have the same measure.

13. Geometry – Arcs, Central Angles, and ChordsP A B
Theorem : if two chords of a circle have the same length, their intercepted arcs have the same measure.

14. Geometry – Arcs, Central Angles, and ChordsP A B
Theorem : if two chords of a circle have the same length, their intercepted arcs have the same measure.
- The reverse is then also true, if intercepted arcs have the same measure, their chord have the same length.

15. Geometry – Arcs, Central Angles, and ChordsP A B
Theorem : if two chords of a circle have the same length, their intercepted arcs have the same measure.
- The reverse is then also true, if intercepted arcs have the same measure, their chord have the same length.
EXAMPLE : CD = AB and the measure of arc AB = 86° What is the measure of arc CD ?

16. Geometry – Arcs, Central Angles, and ChordsP A B
Theorem : if two chords of a circle have the same length, their intercepted arcs have the same measure.
- The reverse is then also true, if intercepted arcs have the same measure, their chord have the same length.
EXAMPLE : CD = AB and the measure of arc AB = 86° What is the measure of arc CD ?

17. Geometry – Arcs, Central Angles, and ChordsX C D P A Y B
Theorem : chords that are equidistant from the center have equal measure

18. Geometry – Arcs, Central Angles, and ChordsX C D P A Y B
Theorem : chords that are equidistant from the center have equal measure
EXAMPLE : XP = YP and the measure of AB = 30. What is the measure of CD ?

19. Geometry – Arcs, Central Angles, and ChordsX C D P A Y B
Theorem : chords that are equidistant from the center have equal measure
EXAMPLE : XP = YP and the measure of AB = 30. What is the measure of CD ?

20. Geometry – Arcs, Central Angles, and ChordsP A X B Y
Theorem : If a diameter or radius is perpendicular to a chord, it bisects that chord and its arc.

21. Geometry – Arcs, Central Angles, and ChordsP A X B Y
Theorem : If a diameter or radius is perpendicular to a chord, it bisects that chord and its arc.
EXAMPLE : PY is perpendicular to and bisects AB, arc AB = 100°.
What is the measure of arc YB ?

22. Geometry – Arcs, Central Angles, and ChordsP A X B Y
Theorem : If a diameter or radius is perpendicular to a chord, it bisects that chord and its arc.
EXAMPLE : PY is perpendicular to and bisects AB, arc AB = 100°.
What is the measure of arc YB ?