circles. points & circle relationships inside the circle the circle outside the circle a c b e g...
TRANSCRIPT
Circles
Points & Circle Relationships Inside the circle THE circle Outside the circle
A
C
B
E
GF
D
Parts of a Circle Center Radius Diameter Chord
Is a diameter a chord?
P
A
B
R
C
D
Parts of a Circle Center: P Radius: PR Diameter: AB Chord: CD & AB
Is a diameter a chord? YES
P
A
B
R
C
D
Construct a Regular Hexagon
1. With a compass – make a circle2. DO NOT CHANGE compass measure
Construct a Regular Hexagon
3. Place point of compass on the circle
Construct a Regular Hexagon
4. Make an arc to the left and right side of the compass on the circle
Construct a Regular Hexagon
5. Move compass to arcs and repeat 4 & 5 until you have 6 marks
Construct a Regular Hexagon
6. 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 Arcsand The Major Arcs…
A
C
B
E
Major & Minor ArcsIdentify the Minor Arcsand The Major Arcs…
Minor Arcs: AB, BC, AC Major Arcs: ABC, BCA, BAC
A
C
B
E
Semicircles An arc that is exactly half the circle.
D
FE
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? A
C
B
12095
P
Arc Measure: Degrees What is the mAB?
A
C
B
12095
P
Arc Measure: Degrees What is the mAB? 120
A
C
B
12095
P
Arc Measure: Degrees What is the mAB? 120 What is the mBC?
A
C
B
12095
P
Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95
A
C
B
12095
P
Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 What is the mAC?
A
C
B
12095
P
Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 What is the mAC? 145
A
C
B
12095
P
Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 What is the mAC? 145 What is the mACB?
A
C
B
12095
P
Arc Measure: Degrees What is the mAB? 120 What is the mBC? 95 What is the mAC? 145 What is the mACB? 240
A
C
B
12095
P
Arc Measure: Length The length is part of the
circumference…so you would have to know the radius.
A
C
B
12095
P
Arc Measure: Length The length is part of the
circumference…so you would have to know the radius.
And the formula
Length = 2r
A
C
B
120955cmdegree
P
Arc Measure: Length
Length = 2r
AB =A
C
B
120955cm
degree
P
Arc Measure: Length
Length = 2r
AB = 25(120/360)A
C
B
120955cm
degree
P
Arc Measure: Length
Length = 2r
AB = 25(120/360) = 10.47 cm A
C
B
120955cm
degree
P
Arc Measure: Length
Length = 2r
AC = A
C
B
120955cm
degree
P
Arc Measure: Length
Length = 2r
AC = 25(145/360) A
C
B
120955cm
degree
P
Arc Measure: Length
Length = 2r
AC = 25(145/360) = 12.65 cm
A
C
B
120955cm
degree
P
Chords and Arcs Theorem What would you think if 2 chords of
a circle had equal length?
A
C D
B
P
Chords and Arcs Theorem What would you think if 2 chords of
a circle had equal length?
A
C D
B
P
AC BD ?
Chords and Arcs Theorem What would you think if 2 chords of
a circle had equal length?
A
C D
B
P
AC BD ?
Prove it!
Chords and Arcs Theorem Draw lines to each point What do you know about the dotted
lines?A
C D
B
P
Chords and Arcs Theorem AP BP (radii of the same O are CP DP
A
C D
B
P
Chords and Arcs Theorem AP BP (radii of the same O are CP DP
A
C D
B
P What do you know about the triangles?
Chords and Arcs Theorem
The ‘s are by SSS
A
C D
B
P
Chords and Arcs Theorem
The ‘s are by SSS
A
C D
B
P So where does this lead…
Chords and Arcs Theorem What do you know about angles 1 &
2?
A
C D
B
P1 2
Chords and Arcs Theorem What do you know about angles 1 &
2?
A
C D
B
P1 2 <1 <2
by CPCTC
Chords and Arcs Theorem So the Central angles are And the arcs formed are
A
C D
B
P