Circles – Central Angles G.C.A.2 Notes Section 12.3 Name__________________

Geometry Page 1 of 2

Arc: an unbroken part of a circle. x Minor Arc: an arc that measures less than 180. x Major Arc: an arc that measures more than 180. x Semicircle: an arc that measures 180.

Name each of the following from the picture.

Minor Arc Major Arc Semicircle Arc Length (Distance) & Arc Angle (Angle Measure)

Adjacent Arcs: arcs of a circle that have exactly one point in common.

Arc Measure: the measure of a arc is the measure of its central angle. The measure of a semicircle is 180.

Arc Addition Postulate: The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. Theorem 12.1: In the same (or in congruent) circle, two arcs are congruent IFF their corresponding central angles are congruent. Central angle of a regular polygon.

𝑚∠𝐶 =360𝑛

where n is the number of sides and ∠𝐶 is the central angle.

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G

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F

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B

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Circles – Central Angles G.C.A.2 Notes Section 12.3 Name__________________

Geometry Page 2 of 2

Complete each equation.

𝑚𝐶𝐸 = 𝑚𝐸𝐹 = 𝑚𝐸𝐶𝐾 = 𝑚𝐷𝐹𝐶 =

𝑚𝐴𝐶 = 𝑚𝐴𝐸 = 𝑚𝐸𝐾 = 𝑚∠𝐾𝐵𝐷 =

Given a regular polygon, complete each equation.

𝑚∠𝐴𝑇𝐵 = 𝑚∠𝐷𝑇𝐵 = 𝑚𝐴𝐶 = 𝑚𝐸𝐶𝐴 = 𝑚∠𝐴𝐸𝐵 = If 𝐴𝐵 = 5 cm, what does 𝑇𝐵 = If 𝐴𝐵 = 5 cm, what does 𝐸𝐴 =

34°

53°

H

K

F

A

C

D

E

70°

39°

K

E

B

A

CD

A

F

E

D

CT

B

A

F

E

D

CT

B

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