Circle Set of all points an equidistant from a given point called the center Radius r Segment that has an endpoint at the center and the other on the circle Diameter d Segment that contains the center and has both endpoints on the circle ID: 494129
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Slide1
10.6 Circles and ArcsSlide2
Circle
Set of all points an equidistant from a given point called the
center
Radius (r)
Segment that has an endpoint at the center and the other on the circle.
Diameter (d)
Segment that contains the center and has both endpoints on the circleSlide3
Congruent Circles
Have congruent radiiSlide4
Central Angle
Angle whose vertex is at the center of the circleSlide5
Arc
Part of the circle
3 types of arcs
Semicircle
Minor Arc
Major ArcSlide6
Semicircle
Half the circle
Measures 180
Named by the 2 endpoints and one other point on the circle.
The endpoints must be listed on the end with the other point in between them.Slide7
Minor Arc
Smaller than a semicircle
Measure of a minor arc is the measure of its corresponding central angle.
Named by 2 endpointsSlide8
Major Arc
Larger than a semicircle
Measure is 360 minus the measure of its related minor arc
Named with 3 letters. The endpoints and a point on the circle between themSlide9
Adjacent Arcs
Two arcs in the same circle that have exactly 1 point in common (beside each other)Slide10
Arc Addition Postulate
The measure of the arcs formed by 2 adjacent arcs is the sum of the measure of the 2 arcsSlide11
Circumference
The distance around the circleSlide12
Theorem 10-9 Circumference of a Circle
The circumference of a circle is
π
times the diameter
C =
π
d
or C = 2πr
radius
diameterSlide13
Examples: Find the circumference of the circles.
a.
C =
π
d
C =
π
(12
)C = 12π inb.C = 2π
rC = 2π (5.3)C = 10.6π
12 in
5.3Slide14
Concentric Circles
Two circles that lie in the same plane and have the same center.Slide15
Example
How much farther do the
outsides of
tires travel?
16.1
in
4.7inSlide16
Find the outside circumference and subtract the inside circumference from it.
Outside circumference
C = 2
π
r
C = 2
π
(16.1)
C = 32.2πInside circumference(first find the inside radius)16.1-4.7=11.4C = 2πrC = 2π(11.4)C = 22.8πD = 32.2π - 22.8π
D = 9.4πSlide17
Arc Length
A fraction of a circles circumference
Ex. If an arc is 30°
Then it is 30/360 = 1/12 of the circle
Therefore it would be 1/12 of the circumference of the circleSlide18
Theorem 10-10 Arc Length
The length of an arc of a circle is the product of the ratio
Measure of arc
360
And the circumference of the circle
Slide19
Example
Find the length of arc XY
16 in
x
Y
P
Angle XPY=90
a.Slide20
X
Y
P
240°
Find the length of arc XPY
15 cm
Example 2Slide21
Congruent arcs
Arcs that have the same measure
and
are in the same circle or in congruent circlesSlide22
CLASSWORK
Pages 654-655
9-27 (all)
30-35 (all)