Post on 12-Jan-2016
1. Draw 4 concentric circles
2. Draw an internally tangent line to two circles3. Name two different types of segments that are equal.
4. Explain the difference between a secant & a chord5. What do you know about a tangent line and the radius drawn to the point of tangency?
P
A
BC
Central Angle : An Angle whose vertex is at the center of the
circleMinor ArcMajor Arc
Less than 180°
More than 180°
ABACB
To name: use 2 letters
To name: use 3 letters
APB is a Central Angle
P
E
F
D
Semicircle: An Arc that equals 180°
EDF
To name: use 3 letters
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
B
C
Q 96
m AB
m ACB
m AE
E
=
=
=
96°
264°
84°
Arc Addition PostulateA
B
C
m ABC =
m AB + m BC
Tell me the measure of the following arcs.
80100
40
140A
B
C
D
R
m DAB =
m BCA =
240
260
Congruent Arcs have the same measure and MUST come from the same circle or of congruent circles.
4545
A
BC
D
110
A
B
C
D
In the same circle, or in congruent circles, two minor arcs are congruent
if and only if their corresponding chords are congruent.
AB CD IFF AB DC
120 120
60
x
x = 60
2x x + 40
2x = x + 40
x = 40
If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
D
A
B
C
R
P
IF: AD BD and AR BR
THEN: CD AB
*YOU WILL BE USING THE PYTHAGOREAN THM. WITH THESE PROBLEMS sometimes*
A
B
C
D
What can you tell me about segment AC if you know it is the perpendicular bisectors of segments DB?
It’s the DIAMETER!!!
Ex. 1 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
y24
x
60x = 24
y = 30
Example 2EX 2: IN P, if PM AT, PT = 10, and PM = 8, find AT.
T
AM
P
MT = 6AT = 12
Example 3In R, XY = 30, RX = 17, and RZ XY.
Find RZ.
R
X
Z
Y
RZ = 8
Example 4 IN Q, KL LZ. IF CK = 2X + 3 and CZ = 4x, find x.
K
Q
C
L
Zx = 1.5
In the same circle or in congruent circles, two chords are congruent if
and only if they are equidistant from the center.
A
B
C
D
M
L
P
AD BC
IFF
LP PM
Ex. 5: In A, PR = 2x + 5 and QR = 3x –27. Find x.
P
R
Q
A
x = 32