Circles

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Circles - PowerPoint PPT Presentation

Circles. Points &amp; Circle Relationships. Inside the circle THE circle Outside the circle. B. G. A. F. E. D. C. Parts of a Circle. R. Center Radius Diameter Chord Is a diameter a chord?. A. C. P. B. D. Parts of a Circle. R. Center: P Radius: PR Diameter: AB

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PowerPoint Slideshow about 'Circles' - elisa

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Circles

Points & Circle Relationships
• Inside the circle
• THE circle
• Outside the circle

B

G

A

F

E

D

C

Parts of a Circle

R

• Center
• Diameter
• Chord

Is a diameter a chord?

A

C

P

B

D

Parts of a Circle

R

• Center: P
• Diameter: AB
• Chord: CD & AB

Is a diameter a chord? YES

A

C

P

B

D

Construct a Regular Hexagon
• With a compass – make a circle
• DO NOT CHANGE compass measure
Construct a Regular Hexagon
• Place point of compass on the circle
Construct a Regular Hexagon
• Make an arc to the left and right side of the compass on the circle
Construct a Regular Hexagon
• Move compass to arcs and repeat 4 & 5 until you have 6 marks
Construct a Regular Hexagon
• Connect the consecutive marks
Major & Minor Arcs
• An Arc is part of a circle.
• Minor Arc is less than half
• Major Arc is more than half

Identify the Minor Arcs

and The Major Arcs…

B

A

E

C

Major & Minor Arcs

B

A

Identify the Minor Arcs

and The Major Arcs…

• Minor Arcs: AB, BC, AC
• Major Arcs: ABC, BCA, BAC

E

)

)

)

)

)

)

C

Semicircles
• An arc that is exactly half the circle.

D

E

F

Measure of Arc

Arcs are measured in two ways

• Degrees
• Length
Arc Measure: Degrees
• The arc measure corresponds the the central angle.

What is the mAB?

B

)

A

120°

95°

P

C

Arc Measure: Degrees

)

• What is the mAB?

B

A

120°

95°

P

C

Arc Measure: Degrees

)

• What is the mAB?

120°

B

A

120°

95°

P

C

Arc Measure: Degrees

)

• What is the mAB?

120°

• What is the mBC?

)

B

A

120°

95°

P

C

Arc Measure: Degrees

)

• What is the mAB?

120°

• What is the mBC?

95°

)

B

A

120°

95°

P

C

Arc Measure: Degrees

)

• What is the mAB?

120°

• What is the mBC?

95°

• What is the mAC?

)

B

)

A

120°

95°

P

C

Arc Measure: Degrees

)

• What is the mAB?

120°

• What is the mBC?

95°

• What is the mAC?

145°

)

B

)

A

120°

95°

P

C

Arc Measure: Degrees

)

• What is the mAB?

120°

• What is the mBC?

95°

• What is the mAC?

145°

• What is the mACB?

)

)

B

A

120°

)

95°

P

C

Arc Measure: Degrees

)

• What is the mAB?

120°

• What is the mBC?

95°

• What is the mAC?

145°

• What is the mACB?

240°

)

)

B

A

120°

)

95°

P

C

Arc Measure: Length
• The length is part of the circumference…

so you would have to know the radius.

B

A

120°

95°

P

C

Arc Measure: Length
• The length is part of the circumference…

so you would have to know the radius.

And the formula

Length = 2pr

B

A

120°

degree°

360

95°

5cm

P

·

C

Arc Measure: Length

degree°

360

Length = 2pr

AB =

·

)

B

A

120°

95°

5cm

P

C

Arc Measure: Length

degree°

360

Length = 2pr

AB = 2p5(120/360)

·

)

B

A

120°

95°

5cm

P

C

Arc Measure: Length

degree°

360

Length = 2pr

AB = 2p5(120/360)

= 10.47 cm

·

)

B

A

120°

95°

5cm

P

C

Arc Measure: Length

degree°

360

Length = 2pr

AC =

·

)

B

A

120°

95°

5cm

P

C

Arc Measure: Length

degree°

360

Length = 2pr

AC = 2p5(145/360)

·

)

B

A

120°

95°

5cm

P

C

Arc Measure: Length

degree°

360

Length = 2pr

AC = 2p5(145/360)

= 12.65 cm

·

)

B

A

120°

95°

5cm

P

C

Chords and Arcs Theorem
• What would you think if 2 chords of a circle had equal length?

B

A

P

C

D

Chords and Arcs Theorem
• What would you think if 2 chords of a circle had equal length?

B

A

P

)

)

AC @ BD ?

C

D

Chords and Arcs Theorem
• What would you think if 2 chords of a circle had equal length?

B

A

P

)

)

AC @ BD ?

Prove it!

C

D

Chords and Arcs Theorem
• Draw lines to each point
• What do you know about the dotted lines?

B

A

P

C

D

Chords and Arcs Theorem
• AP @ BP (radii of the same O are @)
• CP @ DP

B

A

P

C

D

Chords and Arcs Theorem
• AP @ BP (radii of the same O are @)
• CP @ DP

B

A

What do you know about the triangles?

P

C

D

Chords and Arcs Theorem
• The D‘s are @ by SSS

B

A

P

C

D

Chords and Arcs Theorem
• The D‘s are @ by SSS

B

A

P

C

D

Chords and Arcs Theorem
• What do you know about angles 1 & 2?

B

A

P

1

2

C

D

Chords and Arcs Theorem
• What do you know about angles 1 & 2?

B

A

P

<1 @ <2

by CPCTC

1

2

C

D

Chords and Arcs Theorem
• So the Central angles are @
• And the arcs formed are @

B

A

P

C

D