# 9.6 Circles

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Chapter 9, Section 6: Circles

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• 1. Chapter 9 Section 6: Circles March 11, 2009

2. Find Circumference

• ACircleis the set of all points that are the same distance from a given point.
• The given point is theCENTERof the circle.
• Circumference : the distance around the circle.

Center 3. Inside the Circle

• Radius : a line segment that starts on the circle and ends at the center point.
• Chord : segment whose end points are on the circle.
• Diameter : a chord that passes through the center of the circle

4. Pi or

• Pi or , pronounced pie, is the ratio of Circumference (or C) to Diameter (or d).
• C = d
• C/d =
• Pi is constant =3.14159265358979323846
• Pi as a fraction = 22/7
• Because every circle is the same, the ratio is always the same, which is why pi is a constant.

5. Pi

• C =d
• If the d, or diameter, equals 1, then what is the Circumference (or C)?
• C = (1), C =

6. Find the circumference of the circle with a diameter of 6ft.

• C =dthe formula
• C (approx.) = 3.14(6ft)Substitute
• C = 18.84 Simplify!

6 Feet 7. Find the Circumference of Each Circle

• Diameter = 200 miles
• Diameter = 2.8 inches.

• A CENTRAL ANGLE is an angle whose vertex is the center of a circle.
• There are 360 in a circle.
• To make a Pie Graph, find the measure of each central angle by finding the proportion.

9. Use proportions to find the measures of the central angles.

• Juans Weekly Budget :
• Lunch (l) = 25%
• Recreation (r) = 20%
• Clothes (c) = 15%
• Savings (s) = 40%

Find the percentage of 360 to find the degree measurement of the central angles. L = 90 R = 72 C = 54 S = 144 10. AT HOME

• Use a cup opening or cap to make your circles if you dont have a compass.

11. Blood Types of Population

• Tell me the degree measurements of the central angles if you were to make a Pie graph with this information.

43% 5% 12% 40% Type O Type AB Type B Type A 155 18 43 144 12. Students at Western High School: Find Central Angles.

• Students at Western High School work in the following places; restaurants, 140; library, 15; auto shop, 60; retail stores, 75; and other places, 30. Round the measures of the central angles to the nearest degree.

Restaurant: 158 Retail: 84 Auto Shop: 68 Other: 34 Library: 17 13. Assignment #16:

• Pages 472-473: 1-24. Skip #20.
• Remember, if you need a circle and have no compass, then use a cup from home and trace the outside.