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Date:. Sec 10-2 Concept: Arcs and Chords Objective: Given properties of arcs of a circle, solve for missing angles as measured by a s.g. DE. DBE. BD. Vocabulary:. Minor Arc ________ Major Arc _______ Central Angle _______ Semicircle __________. <DPE. Find Each Arc: CD _________

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Date:

Sec 10-2

Concept: Arcs and Chords

Objective: Given properties of arcs of a circle, solve for missing angles as measured by a s.g.


Vocabulary

DE

DBE

BD

Vocabulary:

  • Minor Arc ________

  • Major Arc _______

  • Central Angle _______

  • Semicircle __________

<DPE


Measure of minor arc measure of central angle

Measure of Minor Arc = Measure of Central Angle

148

328

180


Measure of minor arc measure of central angle1

Measure of Minor Arc = Measure of Central Angle

142

218

118

118


AB  BC IFF AB BC

Thm 10-4: In the same or congruent circles, 2 minor arcs are congruent if and only if their corresponding chords are congruent.


Example find mdc given ad 3x dc x 20

X+20

3x

mDC = x+20 =10+20

=30

Example: Find mDC given AD = 3x, DC = x+20

  • 3x= x+20

  • -x -x

  • 2x=20

  • 2

  • X=10


IF PG DF,

Then DE  EF and

DG  GF

Thm 10-5: If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc


AB  CD IFF EG  EF

Thm 10-7: In the same or in congruent circles 2 chords are congruent IFF they are equidistant from the center.


Example ab 12 de 12 ce 7 find cg

6

6

6

6

Example: AB =12, DE =12 , CE = 7, Find CG

Since CG is  AB, AG  GB

Also, CF is  DE, so, DF  FE

Also, if AB = DE, then GC=CF

Use pyth. Thm to find x, that will also be CG.

X2+62 = 72

X2+36 = 49

-36 -36

X2= 13

X=3.6



Date:

Sec 10-3

Concept: Inscribed Angles

Objective: Given an inscribed angle, find arc measures as measured by s.g.


Inscribed angle
Inscribed Angle:

An angle whose vertex is on a circle and whose sides contain chords of the circle.

Intercepted Arc

Inscribed Angle


Example find the measure of the angle

80

x

Example: Find the measure of the angle

Measure of Inscribed Angle = ½ the intercepted Arc

X = ½ the arc

X=1/2(80)

X=40


Find the measure of the arc

x

60

Find the measure of the Arc

Measure of Inscribed Angle = ½ the intercepted Arc

60 = ½ x

½ ½

X=120


Example find the measure of each arc or angle

B

70

B

A

C

C

A

D

mADC = ______

mAC = _______

Example: Find the measure of each arc or angle

180

140


Find the measure of bca

B

72

C

A

Find the measure of <BCA

36

m<BCA = ______


Find m c

B

44

A

C

D

Find m<C

M<C = 44

88





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