Circle Radius Chord Diameter

10.1—Properties of Tangents
Circle—
Radius—
Tangent
Chord
Diameter
Chord—
Radius
Diameter—
Secant
Secant—
Tangent—
Example—
Tell whether the line or segment is best descrbed as a radius, chord, diameter, secant, or tangent of
๏C.
F
a.
E
b.
A
C
B
c.
d.
D
Coplanar circles can intersect in two points, one point, or no points.
Common tangent—
How many common tangents do the circles have? Draw them.
Theorem 10.1—
In ๏G, GH is a radius. Is
I
HI tangent to ๏G?
75
72
G
21
H
In ๏K, J is a point of tangency. Find the radius of ๏K.
K
r
36 cm
r
J
48 cm
Theorem 10.2—
Find x.
25
6x
- 8
L
10.1 Homework
3-10
19.
24.
26.
13.
23.
25.
29.
34.
37.
10.2—Find Arc Measures
Central angle—
central angle
Minor arc—
Major arc—
A
minor arc AB
B
C
Semicircle—
D
major arc ADB
E
Measuring Arcs—
65°
F
G
Measure of a major arc—
Find the measure of each arc of ๏K where HJ is a diameter.
I
a.
J
b.
80°
c.
d.
H
K
Example—a result of a survey about the ages of people in a town are shown. Find the indicated arc
measures.
Ages of People (in years)
T
S
a.
mRU
b.
mRST
c.
mRVT
d.
mUST
>65
17-44
100°
90°
U
Q 80°
60°
45-64
R
15-17
V
Congruent circles—
Congruent arcs—
Tell whether arcs CD and EF are congruent. Why?
a.
D
b.
E
c.
D
E
C
45°
45°
P
C
F
110° Q
C
P
D
F
E
F
10.2 HW PICTURES:
3 – 10
17.
21.
20.
10.3—Properties of Chords
Theorem 10.3—
Theorem 10.4—
Theorem 10.5—
A
Examples—
C
1. In ๏R mAB = _______˚. Find the mCD.
108°
B
2. Use the diagram of ๏C to
find the length of
BF
.
3. In the diagram of ๏P, PV = PW,
QR = 2x + 6, and ST = 3x – 1. Find QR.
R
A
D
15
F
C
B
V
S
Q
P
W
G
D
T
17.
21.
23.
30.
10.4—Inscribed angles and Polygons
Inscribed angle—
A
C
D
B
Intercepted arc—
Theorem 10.7—Measure of an Inscribed Angle Theorem—
A
C
Theorem 10.8—
D
E
B
Theorem 10.9—
R
S
T
--Conversely,
Q
Theorem 10.10—
Examples—
1. Find the indicated measures in ๏X
a. mUW
b. m
V
104°
∠ VWY
33°
X
U
2. Find mWX and m
Y
W
∠ WYX.
X
W
44°
Z
Find the measure of each angle in the quadrilateral.
3.
+ 5)°
(4y
5x
7x
(5y - 5)°
A
Y
10.5—Other Angle Relationships in Circles
A
Theorem 10.11—
D
1
2
Find the indicated measures.
B
C
A
mAB = 124°
D
1
2
B
C
Intersecting lines and circles—if two lines intersect a circle, there are three places where the
lines can intersect
Theorem 10.12—Angles Inside the Circle—
D
E
1
2
F
G
Theorem 10.13—Angles Outside the Circle—
Examples—
Line m is tangent to the circle. Find x or y.
1.
2.
228°
y°
x°
118°
3.
4.
x°
89°
x
63°
44°
30°
5.
39°
(7x - 2)°
(17x + 6)°
10.6—Finding Segment Lengths in Circles
Theorem 10.14—Segments of Chords—
C
A
E
D
B
Find x.
Secant segment—
External segment—
Theorem 10.15—Segments of Secants Theorem—
Find x.
x
Find RT.
T
21
x
R
V
27
10.16—Segments of Secants and Tangents Theorem—
Find x.
x
24
x
x-4
10.7—Write and Graph Equations of Circles
6
Standard Equation of a
Circle Centered at the Origin:
4
2
-10
-5
5
10
-2
-4
-6
-8
Standard Equation of a Circle Centered at (h, k):
3
2
(h, k) 1
-4
-2
2
-1
-2
Write the equations of the circles using the given information.
1.
Center (0, 0), radius 5
2.
Center (-3, 8), radius 5/3
3.
Center (1, 2) and a point on the circle is (4, 2)
4
Graph each equation.
4. x2 + y2 = 25
5. (x - 2)2 + (y + 1)2 = 4