Download Types of Lines [Segments] Radius [of a circle] is • A segment that

Ch 6 Short Summary
Name ____________________________
Chapter 6: Discovering and Proving Circle Properties
Segments:
Types of Lines [Segments]
Radius [of a circle] is
• A segment that goes from
Tangent Properties
Tangent ⊥
N
A
Tangents from a point
E
• The distance from
Diameter [of a circle] is
• A chord that goes through
G
m∠N = 180 −
Chord Properties
If 2 chords are congruent, then
B
D
O
M
• The length of the diameter.
N
A
C
Chord is a segment connecting
Secant A line that
Perpendiculars & Chords
Perpendicular from center bisects
F
O
P
M
Perpendicular bisector of a chord
E
N
H
Tangent [to a circle] is a line that
The point of intersection is called
the
Parallel Chords or Secants
Parallel lines [secants or chords]
intercept
B
A
C
D
G
Ch 6 Short Summary
Name ____________________________
Angles & Arcs:
Arcs & Angles
Vertex?
Formula:
Center
D
Central Angles
central angle An angle whose vertex lies
on the center of a circle and whose sides
are radii of the circle
O
C
A
On
B
Central angle determines the measure of
Inside
Outside
p = m∠AOC , in degrees.
mAC
D
Inscribed Angles
inscribed angle An angle whose vertex lies
on a circle and whose sides
Inscribed Angle Conjecture
The measure of an angle inscribed in a
circle equals
O
B
C
80
O
40
A
R
Inscribed Angles Intercepting Arcs
Conjecture
Inscribed angles that intercept the same
arc [or congruent arcs]
C
A
Arcs
Arc [of a circle] is formed by two points on
a circle and a continuous part of the circle
between them. The two points are called
endpoints.
Arc Addition Postulate If point B is
AC and between points A and C, then
on p
p
p = mAC
p.
mAB + mBC
Semicircle is an arc whose endpoints are
Minor arc is an arc that is
L
100
J
50
50
M
Major arc is an arc that is
K
Angles Inscribed in a Semicircle
Conjecture
Angles inscribed in a semicircle
Intercepted Arc An arc that lies in the
interior of an angle with endpoints on
C
90
E
D
Ch 6 Short Summary
Circles
Circle is a set of points in a plane a
given distance (radius) from a given
point (center).
Sphere is a set of points a given
distance (radius) from a given point
(center).
Congruent circles are two or more
circles
Concentric circles are two or more
circles
Tangent Circles Circles that are
tangent to the same line at the same
point.
Internally Tangent Circles Two
tangent circles having centers on the
same side of their common tangent.
Externally Tangent Circles Two
tangent circles having centers on
opposite sides of their common
tangent.
Name ____________________________
Circumference & Arc Length
A
O
60
5
B
Circumference
The perimeter of a circle, which is the
distance
Also the curved path of the circle itself.
Circumference Conjecture
If C is the circumference, d = diameter,
r = radius:
C=
Measure of an Arc: The measure of an arc
equals
VS
Arc length: The portion of (or fraction of)
the circumference of the circle described
by an arc, measured in units of length.
Arc Length Conjecture
Arc length =
Ch 6 Short Summary
Name ____________________________
Quadrilaterals
Cyclic Quadrilateral A quadrilateral that can
be
A
C
B
D
Cyclic Quadrilateral Conjecture
The opposite angles of a cyclic quadrilateral
Parallelogram Inscribed in a Circle
Theorem
If a parallelogram is inscribed within a
circle, then the parallelogram
G
O
Y
D
L