Circles

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Circle
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Circle Definition
Circle
The set of points coplanar points equidistant
from a given point.
The given point is called the CENTER of the
circle.
The distance from the center to the circle is
called the RADIUS.
Center
Radius
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Definitions
Chord
The segment whose endpoints lie on the circle.
A chord that contains the center of the circle.
Diameter
Tangent
A is a line or line segment that touches a circle
at one point only .
Tangent
Point of Tangency
Chord
The point where the tangent line intersects the
circle.
Diameter
Secant
A line that intersects a circle at two points. It
is a line, ray, or segment that contains a chord
of a circle.
Secant
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Definitions
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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Polygons
Inscribed Polygon

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

Circumscribed Polygon
A polygon whose sides are tangent to a circle.
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ARCS

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

Arcs
If a circle is divided into two unequal parts,
the longer arc is called the major arc and the
shorter arc is called the minor arc.
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• An angle with its vertex on a circle that is
  formed by two other points on the circle is
  called an inscribed angle.

For an inscribed angle with the same endpoints as
a central angle, the inscribed angle is half the
central angle.
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• If arc Q is 3 cm long in the circle above, and
  the circumference of the circle is 9 cm, then
  what is the measurement of the central angle?

3 cm/9 cm 1/3
The central angle will be the same fraction of
360. (All circles measure 360.).
Therefore, set up a ratio to solve for the
central angle measurement.
The central angle equals 120.
1/3 X/3601/3 120/360
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• In the circle above, arc Q is 30 mm long. The
  circumference of the circle is 90 mm. What is the
  measurement of the central angle?

30 mm / 90 mm 1/3
The central angle will be the same fraction of
360. (All circles measure 360.).
Therefore, set up a ratio to solve for the
central angle measurement.
The central angle equals 120.
1/3 X/3601/3 120/360
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• Given a circle with center B and ABC 74,
  determine the measure of AKC.

For an inscribed angle with the same endpoints as
a central angle, the inscribed angle is half the
central angle.
AKC 1/2 ABC 1/2 74
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Inscribed Angle
The Angle AKC 37.
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• Segment AC is the diameter of the circle.
• If the length of segment BD 7 inches, find the
  length of segment BE.

Segment DE is perpendicular to the diameter AC.
Therefore, segment DE is bisected by segment
AC. So, the length of segment BE is equal to
the length of segment DB.
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??
BE 7 inches