Geometry

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Geometry

• 9.1 An Introduction to Circles

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Circle

• The set of all points in a plane at a given
• distance from a given point.

. P
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P is the center of the circle.
The circle is the set of all points in the plane
of the screen 3 away from P.
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Radius Plural is radii

• A segment that joins the center of the
• circle to any point on the circle.

. P
radius
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Chord

• A segment whose endpoints lie on a circle.

. P
chord
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Diameter

• A chord that passes through the center
• of the circle.

twice
The diameter is _________ as long as the
radius.
. P
diameter
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Secant

• A line that contains a chord of a circle.

. P
SECANT
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Tangent

• A line in the plane of a circle that
• intersects the circle in exactly one point.

. P
Tangent
.
Point of tangency
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Name
1) The center
A
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Name
2) Two diameters
DB
and
FC
10
Name
3) A point of tangency
D
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Name
4) Four radii
AB
and
AF
and
AC
AD
and
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Name
5) A tangent
ED
13
Name
6) A secant
FC
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Name
7) Six chords
FB
and
and
DF
DC
and
and
and
BC
DB
FC
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8) Why is AC not a Chord of A
.
A chord is a segment with both endpoints on the
circle.
AC has only one endpoint on the circle.
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9) Why is BD not a Chord of A
.
A chord is a segment not a line.
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Sphere

• Sphere The set of all points in space given
  distance from any given point is a sphere.
• Many of the terms used with circles are also used
  with spheres.
• For example, sphere X has a center
  
  radii
  
  chords
  diameter
  secants
  
  tangent
  point of tangency

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Congruent Circles
congruent circles/spheres Circles (or spheres)
are congruent if they have congruent radii.
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Concentric Circles
concentric circles Circles that lie in the same
plane and have the same center are concentric.
concentric spheres Concentric spheres have
the same center.
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Inscribed Polygon

• A polygon is inscribed in a circle if each vertex
  of the polygon lies on the circle.
• A circle is circumscribed about a polygon if each
  vertex of the polygon lies on the circle.

The polygon is inscribed in the circle.
Thus, the circle is circumscribed about the
polygon.
These two sentences have the same meaning.
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F
C
G
D
In sphere A, draw 10. a diameter, BC 11. a
chord, DE 12. a tangent, CF 13. a secant, DG
B
C
E
D
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• 14. Draw two concentric circles. Draw a tangent
  to one of the circles. Is it tangent to the other
  circle?
• 15. Draw a large circle. Inscribe an isosceles
  triangle in the circle.
• 16. Draw a rectangle. Circumscribe a circle about
  the rectangle.

No.
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Find the value of x.
6
6
60
3
90
3v3
30
3v3
3v3
x 6v3
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Find the value of x. O is the center of each
circle.
x 8
x 5
x
x 4v2
10
x
45?
O
x 5v2
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HW

• P. 330-340 CE 1-11 WE 1-15