Math II

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Math II
UNIT QUESTION What special properties are found
with the parts of a circle? Standard MM2G1,
MM2G2 Todays Question What are the parts of a
circle? Standard MM2G3.a,d
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Parts of a Circle
Circle set of all points _________ from a given
point called the _____ of the circle.
equidistant
C
center
Symbol
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CHORD a segment whose ________ are on the circle
endpoints
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Radius
RADIUS distance from the _____ to a point on the
circle
center
P
5
Diameter
DIAMETER distance ______ the circle through its
______
across
P
center
Also known as the longest chord.
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What is the relationship between the diameter and
the radius of a circle?
r OR D
½ D
2 r
7
D ?
32
24
12
r ?
16
r ?
4.5
6
D ?
12
9
8
Use ?P to determine whether each statement is
true or false.
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Secant Line
A secant line intersects the circle at exactly
TWO points.
SECANT sounds like second
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TANGENT a LINE that intersects the circle
exactly ONE time
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Point of Tangency
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Name the term that best describes the line.
Secant
Radius
Diameter
Chord
Tangent
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Two circles can intersect

• in two points
• one point
• or no points

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No points of intersection (different center)
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No points of intersection (same center)
Concentric Circles
Same center but different radii
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1 point of intersection(Tangent Circles)
Externally Tangent
Internally Tangent
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2 points of intersection
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Common Tangents
Internal
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Common Tangents
External
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A point is inside a circle if its distance from
the center is less than the radius.
INTERIOR
?
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EXTERIOR
?
A point is outside a circle if its distance from
the center is greater than the radius.
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A point is on a circle if its distance from the
center is equal to the radius.
?
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Point of Tangency
If a line (segment or ray) is tangent to a
circle, then it is perpendicular to the radius
drawn to the point of tangency.
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1. Find x
A
12
B
9
a2 b2 c2
x
92 122 x2
x 15
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2. Find RQ
a2 b2 c2
122 (QR)2 (812)2
P
122 (QR)2 202
12
8
RQ 16
R
Q
26
r2 242 (r 16)2
3. Find the radius.
r2 576 r2 32r 256
320 32r
16
r 10
A
C
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B
27
S
If two segments from the same exterior point are
tangent to a circle, then they are congruent.
R
T
28
4. Find x
R
S
T
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5. Find x
C
A
B
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6. Find x.
B
A
C
P
D
E
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7. Find NP
N
T
S
P
R
Q
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CW Workbook Page 198 1-10 and Page 199 18-33
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HW Page 186 1-22