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10.2 Find Arc Measures. Central Angle – an angle whose vertex is the center of a circle. A. C. B. Central Angles.  ACB is a central angle. Arcs. Arc - a piece of a circle. - named with 2 or 3 letters - measured in degrees

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Central Angle – an angle whose vertex is the center of a circle

A

C

B

Central Angles

ACB is a central angle


Arcs

Arc - a piece of a circle.

- named with 2 or 3 letters

- measured in degrees

Minor Arc - part of a circle that measures less than 180o (named by 2 letters).

A

B

B

(

BP

P


More arcs
More Arcs

Major Arc - part of a circle that measures between 180o and 360o. Named with three letters

Semicircle – an arc whose endpoints are the endpoints of a diameter of the circle (or ½ of a circle)

CPS

A

B

(

(

ABC or CBA

C

C

P

(

S


Arc measures
Arc Measures

Measure of a Minor Arc – equals the measure of its central angle

Measure of a Major Arc – equals 360o minus the measure of the minor arc


Example find the arc measures
example: find the arc measures

(

m AB =

m BC =

m AEC =

m BCA

50o

E

(

130o

(

180o

A

180o

(

50o

=180o+130= 310o

130o

C

or

360o - 50o = 310o

B


Arc a ddition p ostulate
Arc Addition Postulate

The measure of an arc formed by two adjacent arcs is the sum of the measures of those arcs.

B

A

C

(

(

(

m AB + m BC = mABC


Congruency among arcs
Congruency Among Arcs

Congruent Arcs - 2 arcs with the same measure and the same length

They MUST be from the same circle or  circles!!!


Example
Example

(

m AB = 30o

(

A

m DC = 30o

(

(

AB  DC

30o

E

B

D

30o

C


Example continued
example continued

(

mBD = 45o

A

(

mAE = 45o

B

(

(

BD  AE

45o

The arcs are the same measure; so, why aren’t they ?

C

D

E

The 2 circles are NOT  !


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