Circles

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Circles
Modified by Lisa Palen
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Definitions
The set of points in a plane at a given distance
from a given point in that plane.
Symbol
Circle
The CENTER of the circle is the point that is the
same distance to every point on the circle.
The distance from the center to the circle is
called the RADIUS as well.
The RADIUS is a segment from the center of the
circle to a point on the circle.
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Definitions
Chord
A segment whose endpoints lie on the circle.
Chord
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Definitions
Chord-
A segment whose endpoints lie on the circle.
Chord
Diameter-
A chord that contains the center of the circle.
Diameter
The DIAMETER of a circle is the length of any
diameter as well.
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Definitions
Chord-
A segment whose endpoints lie on the circle.
Chord
Diameter-
A chord that contains the center of the circle.
Diameter
Secant
The DIAMETER of a circle is the length of any
diameter as well.
A line that contains a chord.
Secant-
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EXAMPLE

• Identify the chords, radii, and diameters.

J
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Definitions
Tangent
Tangent
A line in the plane of the circle that intersects
the circle in exactly one point.
Point of Tangency
The point where the tangent line intersects the
circle.
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Definitions
CommonTangent
A line in the plane of two or more circles that
is tangent to each circle.
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Definitions
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Congruent circles- circles that have congruent
radii.
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Concentric circles- circles that lie in the same
plane and have the same center.
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INSCRIBED POLYGON

• A polygon inside a circle whose vertices lie on
  the circle.

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CIRCUMSCRIBED POLYGON

• A polygon whose sides are tangent to a circle.

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ARC

• The part or portion on the circle from some point
  B to C is called an arc.

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ARCS

• Identify two different arcs.

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ARC MEASURE

• Central angle angle with vertex the center of
  a circle, with rays that intersect the circle
• The arc measure is the degree measure of the
  arcs central angle.
• An arcs central angle
• is the angle with vertex
• the center of the circle
• and rays passing
• through the arcs
• endpoints.

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MINOR AND MAJOR ARCS

• A minor arc is an arc that measures less than
  180
• A major arc is an arc that measures more than
  180

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SEMICIRCLE

• An arc that measures 180.

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ARCS

• Identify a minor arc, a major arc, and a
  semicircle, given that segment CD is a diameter.
  

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NAMING ARCS

• A minor arc is named using its endpoints with an
  arc above.
• A major arc (or semicircle) is named using its
  endpoints along with another point on the arc (in
  order).

or
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NAMING ARCS

• How many different arcs can you name?

NOTE the chord EF is not a diameter.
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ARC MEASURE NOTATION

• The arc measure is written
• It is equal to the measure of the corresponding
  central angle.

Central Angle
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ADJACENT ARCS

• Two arcs of a circle that intersect at exactly
  one point.
• and
• are adjacent.

B
C
A
D
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ARC ADDITION POSTULATE

• The measure of an arc formed by two adjacent arcs
  is the sum of the measures of the two arcs.