10-6 full day circles and arcs 2011 - poudre school...
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106 Full Day Circles and Arcs 2011
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Warm Up
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What is a circle? How would you describe a circle in
words so I can draw it?
A
A circle is the set of all points equidistant from a given point called the center.
You name a circle by its center.
WarmUp
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Objective: Find the measures of central angles and arcs. Find circumference and arc length.
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P
AC
Q
B
P
A CA radius is a segment that has one endpoint at the center and the other endpoint on the circle.
A diameter is a segment that contains the center of a circle and has both endpoints on the circle.
How do we define AC? AP?
How do we define PQ? BC?
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P
A C
Congruent circles have congruent radii.
A central angle is an angle whose vertex is the center of the circle.
P
A C
PAC
m PAC = mCP
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This study shows how people spend their time.
What is the measure, in degrees, of the central angle used for the Entertainment section?
What is the measure, in degrees, of the central angle used for the Sleep and Food section?
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Identifying Arc's.
An arc is a part of a circle.
semicircle minor arc major arc
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What is the Circumference of a circle?
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What is pi?
Pi is the ratio of the circumference of a circle to its diameter.
= CdHow would you solve this equation for C?
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Circles that lie on the same plane and have the same center are concentric circles.
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A car has a turning radius of 16.1 ft. The distance between the two front tires is 4.7 ft. In completing the outer turning circle, how much farther does a tire travel than a tire on the concentric inner circle?
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The diameter of a bicycle wheel is 22 in. To the nearest whole number, how many revolutions does the wheel make when the bicycle travels 100 ft?
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The measure of an arc is in degrees while the arc length is a fraction of a circle's circumference.
What fraction of the circle's circumference is a 60o angle?
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Find the length of each arc shown in pink. Leave your answer in terms of pi.
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Find the length of a semicircle with radius 1.3 m. Leave your answer in terms of pi.
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It is possible for two arcs of different circles to have the same measure but different lengths.
In order for two arcs to be CONGRUENT ARCS, they must have the same measure AND the same length.
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Homeworkpg. 569 #126, 2838 even, 4247, 59, 71
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