Arcs and Central Angles

1. ARCS AND CENTRALS ANGLES

2. O
C B
O
A
B

3. Semicircle – a part of a circle from one end point of the diameter to
the other endpoint. It is half of the circle.
Definition of Parts of a Circle
The degree measure of semicircle 180º.

4. Central angle – is an angle whose vertex is the center of
the circle.
- Central angle separates a circle into two
arcs called minor arcs and major arcs.
∠AOB

5. Central Angle
∠AOB
Minor Arc
AB
Minor arc AB -
Major Arc
The degree measure of a minor arc - is equal to the measure of the
central angle.
Is smaller than a semicircle.

6. Example:
m∠AOB = 45º ,
45º
AB = 45º
Minor Arc
AB
45º
m

7. Central Angle
∠AOB
Minor Arc
AB
Major arc ACB - Is larger than a semi circle.
Major Arc
ACB
The degree measure of a major arc - is equal to 360 minus the
degree measure of its related minor arc.

8. Example:
m ACB= 360º m AB = 45º
Find the measure of major arc
m ACB= 360º - 45º
m ACB= 315º

9. Arc Addition Postulate
The measure of an arc formed by
two adjacent, non overlapping
arc is the sum of the measures of
two arcs.

11. b. Find m ADC
a. Find m ABC
m ABC = m AB + m BC
= 55º + 70º
= 125º
m ADC = 360º - 125º
=235º
m ADC = m AD + m DC
OR = 195º + 40º
= 235º

12. Congruent Arcs
In congruent circles, arcs which have the same measure are
congruent arcs
Theorem
If two minor arcs of a circle or of congruent circles are congruent,
then the corresponding chords are congruent.

14. STATEMENTS REASONS
1. Circle O with AB ≅ CD
2. mAB = mCD
3. m∠AOB = mAB
4. OA ≅ OC
OB ≅ OD

15. SUMMARY

20. Thank you