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Circles
Vocabulary
And
Properties
Circle
A set of all points in a plane at a given
distance from a given point in the
plane.
.
Radius
A segment from a point on the circle to
the center of the circle.
Congruent Circles
Two circles whose radii have the same
measure.
R=3 cm
R=3 cm
Concentric Circles
Two or more circles that share the same
center.
.
Chord
Is a segment whose endpoints lie on the
B
circle.
A
D
C
Diameter
A chord passing through the center of a
circle.
I
J
Secant
A line that contains a chord.
Tangent
A line in the plane of the circle that
intersects the circle in exactly one point.
Semicircle
A semicircle is an arc of a circle whose
endpoints are the endpoints of the
diameter.
A
AB Is a semicircle
B
Minor Arc
An arc of a circle that is smaller than a
semicircle. The minor arc is AP
(clockwise) or PD (clockwise).
P
A
D
Major Arc
An arc of a circle that is larger than a
semicircle. The major arc would be PA
(clockwise) or DP (counter clockwise).
P
A
D
Inscribed Angle
An angle whose vertex lies on a circle and
whose sides contain chords of a circle.
A
C
B
D
Central Angle
An angle whose vertex is the center of
the circle.
A
B
O
Properties of Circles
The measure of a central angle is two
times the measure of the angle that
subtends the same arc.
Example
B
A
O
C
If the m<C is 55,
then the m<O is
110. Both angle C
and angle O subtend
the same arc, AB.
Property #2
Angles inscribed in the same arc are
congruent.
Example
A
The m<AQB and the
m<APB are congruent
because they both
inscribe arc AB.
B
Q
P
The m<QAP and m<QBP
would be congruent
because they inscribe
arc QP.
Property #3
Every angle inscribed in a semicircle is an
right angle.
Example
C
Each of the three
angles inscribed in
the semicircle is a
right angle.
D
B
A
E
Angle B, C, and D are all 90
degree angles.
Property #4
The opposite angles of a quadrilateral
inscribed in a circle are supplementary.
Example
The measure of angle D + angle B=180
The measure of angle C+angle A=180
B
65
A 70
115
D
110 C
Property #5
Parallel lines intercept congruent arcs on
a circle.
Example
Arc AB is congruent to Arc CD
A
B
D
C
Formulas
What are the two formulas for finding
circumference?
C=
C=
Answer
C=2 pi r
C=d pi
Area of a circle
A=?
Answer
A=radius square times pi
The End
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