Chapter 12 Circles

1
Chapter 12Circles

• Sec. 12 1
• Tangent Lines

Objectives 1) To use the relationship
between a radius and a tangent. 2) To use the
relationship between 2 tangents from one point.
2
Circle Is the set of all points in a plane that
are a given distance from a given point.
Center

• Name the circle after its center.
• Ex OP

• Chord A segment whose endpts lie on the circle.
• Ex. TA

T
A
Radius A segment that has one endpt at the
center the other endpt on the circle.
P
C
D
B

• BP
• All Radii are ?

• Diameter A chord that contains the center of
  the circle.
• Ex CD

3
Tangent
B
P
C
D
Y
Tangent Line A line in the plane of the circle
that intersects the circle in exactly one point.

• Point of Tangency
• Ex Y

4

• Th(11 1) If a line is tangent to a circle,
  then the line is ? to the radius at the point of
  tangency.
• OP ? AB

O
A
P
B
5
Ex.1 Find the missing ? measure.

• m?A m?B m?C 180
• x 90 22 180
• x 68

A
x
22
C
B
6
Ex.2 Find the m?x

• DE and EF are tangent to circle C.

Top Triangle m?C m?D m?E 180 55 90 m?E
180 m?E 35 Bottom Triangle m?C m?F m?E
180 55 90 m?E 180 m?E 35
D
90
55
x
110
E
C
90
F
m?x 70
7
Ex.3 Finding distance between centers
12in
4in
12in
6in
4in
10in
a2 b2 c2 62 122 c2 c 13.4in
8
Ex.4 Is a line tangent to circle N

• Is LM tangent to circle N?
• If so then ?LNM is right
• ?L will be the right angle

a2 b2 c2 72 242 252 49 576 625 625
625
N
Yes it is tangent!
25
7
M
24
L
9
Ex.5 Solve for x
N
6
x
6
M
8
a2 b2 c2 62 82 (6x)2 36 64 36 6x
6x x2 100 x2 12x 36 0 x2 12x - 64
L
Factor this! (x 4) and (x 16) x 4 and x
-16
10
Inscribed vs Circumscribed

• Inscribed
• Inside of the circle

• Circumscribed
• Outside of circle

? tangent to the circle in 3 places.
11

• Th(11-3) 2 segments tangent to a circle from a
  point outside the circle are ?.
• AB ? AC

B
A
C
12
Ex.5 Solve for x, y, z
x 10 y 4 z 8
4
y
8
10
z
x
Find the perimeter of the ?.
44