1. Parts of a CircleParts of a Circle
You will learn to identify and use parts of circles.
1) circle
2) center
3) radius
4) chord
5) diameter
6) concentric

2. Parts of a CircleParts of a Circle
A circle is a special type of geometric figure.
All points on a circle are the same distance from a ___________.center point
O
B
A
The measure of OA and OB are the same; that is, OA  OB

3. Parts of a CircleParts of a Circle
Definition
of a
Circle
A circle is the set of all points in a plane that are a given
distance from a given _____ in the plane, called the
______ of the circle.
point
center
P
Note: a circle is named by its center. The circle above is named circle P.

4. Parts of a CircleParts of a Circle
There are three kinds of segments related to circles.
A ______ is a segment whose endpoints are the center of the circle and a
point on the circle.
radius
A _____ is a segment whose endpoints are on the circle.chord
A ________ is a chord that contains the centerdiameter

5. Parts of a CircleParts of a Circle
Segments
of
Circles
K
A
diameterchordradius
R
K
J
K
T
G
KA is a radius
of K
JR is a chord
of K
GT is a diameter
of K
From the figures, you can not that the diameter is a special type of _____
that passes through the center.
chord

6. Parts of a CircleParts of a Circle
C
A
D
B
Q
AD is a diameter of Q .
Use Q to determine whether each statement is true or false.
False;
Segment AD does not go
through the center Q.
AC is a chord of Q .
True;
AD is a radius of Q .
False;

7. Theorem
11-1
Theorem
11-2
Parts of a CircleParts of a Circle
All radii of a circle are _________.congruent
P
R
S
T
G
PR≃PG≃PS≃PT
The measure of the diameter d of a circle is twice the
measure of the radius r of the circle.
d = 2r
or
1
2
d= r

8. Parts of a CircleParts of a Circle
C
A
B
Q
3x-5
17
Find the value of x in Q.
3x – 5 = 2(17)
3x – 5 = 34
3x = 39
x = 13

9. Parts of a CircleParts of a Circle
If QR = 1, find RT
RT = TQ – QR
RP Q T
BA
P has a radius of 5 units, and T has a radius of 3 units.
RT = 3 – 1
RT = 2
If QR = 1, find PQ
PQ = PR – QR
PQ = 5 – 1
PQ = 4
If QR = 1, find AB
AB = 2(AP) + 2(BT) – 1
AB = 2(5) + 2(3) – 1
AB = 10 + 6 – 1
AB = 15

10. Parts of a CircleParts of a Circle
If AR = 2x, find AP in terms of x.
AR = 2(AP)
RP Q T
BA
P has a radius of 5 units, and T has a radius of 3 units.
2x = 2(AP)
x = AP
If TB = 2x, find QB in terms of x.
QB = 2(TB)
QB = 2(2x)
QB = 4x

11. S
Parts of a CircleParts of a Circle
Because all circles have the same shape, any two circles are similar.
However, two circles are congruent if and only if (iff) their radii are _________.congruent
Two circles are concentric if they meet the following three requirements:
Circle R with radius RT and
circle R with radius RS are
concentric circles.
 They lie in the same plane.
 They have the same center.
 They have radii of different lengths.
R
T