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Circles - PowerPoint PPT Presentation


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

B

G

A

F

E

D

C

parts of a circle
Parts of a Circle

R

  • Center
  • Radius
  • Diameter
  • Chord

Is a diameter a chord?

A

C

P

B

D

parts of a circle1
Parts of a Circle

R

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

Is a diameter a chord? YES

A

C

P

B

D

construct a regular hexagon
Construct a Regular Hexagon
  • With a compass – make a circle
  • DO NOT CHANGE compass measure
construct a regular hexagon1
Construct a Regular Hexagon
  • Place point of compass on the circle
construct a regular hexagon2
Construct a Regular Hexagon
  • Make an arc to the left and right side of the compass on the circle
construct a regular hexagon3
Construct a Regular Hexagon
  • Move compass to arcs and repeat 4 & 5 until you have 6 marks
construct a regular hexagon4
Construct a Regular Hexagon
  • Connect the consecutive marks
major minor arcs
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 arcs1
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
Semicircles
  • An arc that is exactly half the circle.

D

E

F

measure of arc
Measure of Arc

Arcs are measured in two ways

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

What is the mAB?

B

)

A

120°

95°

P

C

arc measure degrees1
Arc Measure: Degrees

)

  • What is the mAB?

B

A

120°

95°

P

C

arc measure degrees2
Arc Measure: Degrees

)

  • What is the mAB?

120°

B

A

120°

95°

P

C

arc measure degrees3
Arc Measure: Degrees

)

  • What is the mAB?

120°

  • What is the mBC?

)

B

A

120°

95°

P

C

arc measure degrees4
Arc Measure: Degrees

)

  • What is the mAB?

120°

  • What is the mBC?

95°

)

B

A

120°

95°

P

C

arc measure degrees5
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 degrees6
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 degrees7
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 degrees8
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
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 length1
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 length2
Arc Measure: Length

degree°

360

Length = 2pr

AB =

·

)

B

A

120°

95°

5cm

P

C

arc measure length3
Arc Measure: Length

degree°

360

Length = 2pr

AB = 2p5(120/360)

·

)

B

A

120°

95°

5cm

P

C

arc measure length4
Arc Measure: Length

degree°

360

Length = 2pr

AB = 2p5(120/360)

= 10.47 cm

·

)

B

A

120°

95°

5cm

P

C

arc measure length5
Arc Measure: Length

degree°

360

Length = 2pr

AC =

·

)

B

A

120°

95°

5cm

P

C

arc measure length6
Arc Measure: Length

degree°

360

Length = 2pr

AC = 2p5(145/360)

·

)

B

A

120°

95°

5cm

P

C

arc measure length7
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
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 theorem1
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 theorem2
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 theorem3
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 theorem4
Chords and Arcs Theorem
  • AP @ BP (radii of the same O are @)
  • CP @ DP

B

A

P

C

D

chords and arcs theorem5
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 theorem6
Chords and Arcs Theorem
  • The D‘s are @ by SSS

B

A

P

C

D

chords and arcs theorem7
Chords and Arcs Theorem
  • The D‘s are @ by SSS

B

A

P

So where does this lead…

C

D

chords and arcs theorem8
Chords and Arcs Theorem
  • What do you know about angles 1 & 2?

B

A

P

1

2

C

D

chords and arcs theorem9
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 theorem10
Chords and Arcs Theorem
  • So the Central angles are @
  • And the arcs formed are @

B

A

P

C

D