6.1 circles---day-28-1
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2 5 2 . 5 15 8 . 4 10 7 . 3 12 . 2 14 5 . 1 2 2 2 2 2 x x x x x x x x x x Factor Warm – up Session 28 2 7 x x 4 3 x x 2 5 x x 3 5 x x 2 1 2 x x
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Transcript of 6.1 circles---day-28-1
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Math IIDay 28 (9-17-09)
UNIT QUESTION: What special properties are found with the parts of a circle?Standard: MM2G1, MM2G2
Today’s Question:What are the parts of a circle?Standard: MM2G3.a,d
AGENDA1. Notes 6.1 - Circles2. Class Work3. Home Work
Friday 9/17
6.2
Parts of a Circle
Circle – set of all points _________ from a given point called the _____ of the circle.
C
Symbol:
equidistant
center
C
CHORD: a segment whose ________ are on the circle
endpoints
P
RADIUS: distance from the _____ to a point on the circle
center
Radius
Diameter
P
DIAMETER: distance ______ the circle through its ______
center
across
Also known as the longest chord.
What is the relationship between the diameter and the radius of a circle?
r =
OR
D =
½ D
2 r
D = ?
r = ?
r = ? D = ?
Use P to determine whether each statement is true or false.
P
Q
R
TS
diameter. a is .1 RT False
radius. a is .2 PS True
chord. a is .3 QT True
Secant Line
A secant line intersects the circle at exactly TWO points.
TANGENT: a LINE that intersects the circle exactly ONE
time
Point of Tangenc
y
Name the term that best describes the line.
Secant
Radius
DiameterChord
Tangent
Two circles can intersect…
•in two points
•one point
•or no points
No points of intersection (different center)
No points of intersection (same center)
Same center but different radii
1 point of intersection(Tangent Circles)
Internally Tangent
Externally Tangent
2 points of intersection
INTERIOR
A point is inside a circle if its distance from the center is less than the radius.
EXTERIOR
A point is outside a circle if its distance from the center is greater than the radius.
A point is on a circle if its distance from the center is equal to the radius.
If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.
Point of Tangenc
y
More Pythagorean Theorem type problems! Yeah!!
a2 + b2 = c2
x = 15
92 + 122 = x2
a2 + b2 = c2
RQ = 16
122 + (QR)2 = (8+12)2
122 + (QR)2 = 202
r2 + 242 = (r + 16)2
r = 10
r2 + 576 = r2 + 32r + 256320 = 32r
R
S
T
TSRS If two segments from
the same exterior point are tangent to a circle, then they are
congruent.
Party hat problems!
R
S
T
22 x
11 1122 x92 x
3 3 xorx
A
C
B152 x
x14
15x
AC
E
3
4
7X
B
D
X
P
TS
Q10 4
18NP
P
N
R
12
