Download Arcs and Chords march 27-1misk2p

1. Draw 4 concentric circles
2. Draw an internally tangent line to two circles
3. Name two different types of segments that are
equal.
4. Explain the difference between a secant & a chord
5. What do you know about a tangent line and the
radius drawn to the point of tangency?
Central Angle :
An Angle whose vertex is at the center of the circle
A
Major Arc
Minor Arc
More than 180°
Less than 180°
P
ACB
To name: use
3 letters
AB
C
B
APB is a Central Angle
To name: use
2 letters
Semicircle: An Arc that equals 180°
E
D
To name: use
3 letters
EDF
P
F
You try…
10.2
Practice B
1-8
D
E
A
C
B
F
THINGS TO KNOW AND
REMEMBER ALWAYS
A circle has 360 degrees
A semicircle has 180 degrees
Vertical Angles are Equal
measure of an arc = measure of central angle
A
E
Q
m AB = 96°
m ACB = 264°
m AE = 84°
96
B
C
Arc Addition Postulate
A
C
B
m ABC = m AB + m BC
Tell me the measure of the following arcs.
m DAB = 240
m BCA = 260
D
C
140
R
40
100
80
B
A
You try…
10.2
Practice B
9 – 18
M
N
O
82
R
63
Q
P
Congruent Arcs have the same measure and
MUST come from the same circle or of
congruent circles.
C
B
45
A
45
D
110
In the same circle, or in congruent circles,
two minor arcs are congruent if and only if
their corresponding chords are congruent.
B
C
A
D
AB  CD IFF AB  DC
60
120
120
x
x = 60
2x
2x = x + 40
x = 40
x + 40
If a diameter of a circle is perpendicular to a
chord, then the diameter bisects the chord and
its arc.
IF: AD  BD and AR  BR
C
P
A
THEN: CD  AB
R
B
D
*YOU WILL BE USING THE PYTHAGOREAN THM. WITH THESE PROBLEMS sometimes*
What can you tell me about segment AC if
you know it is the perpendicular bisectors of
segments DB?
D
It’s the
DIAMETER!!!
A
C
B
Ex. 1 If a diameter of a circle is
perpendicular to a chord, then the diameter
bisects the chord and its arc.
x = 24
y = 30
24
y
60
x
Example 2
EX 2: IN P, if PM  AT, PT = 10,
and PM = 8, find AT.
A
P
M
T
MT = 6
AT = 12
Example 3
In R, XY = 30, RX = 17, and RZ  XY.
Find RZ.
X
R
Y
Z
RZ = 8
Example 4
IN Q, KL  LZ.
IF CK = 2X + 3 and
CZ = 4x, find x.
Q
Z
C
L
x = 1.5
K
In the same circle or in congruent circles,
two chords are congruent if and only if they
are equidistant from the center.
B
AD  BC
A
IFF
M
P
LP  PM
L
C
D
Ex. 5: In A, PR = 2x + 5 and
QR = 3x –27. Find x.
R
A
P
Q
x = 32
Ex. 6: IN K, K is the midpoint of RE.
If TY = -3x + 56 and US = 4x, find x.
U
T
K
E
R
Y
S
x=8