1. PRE-ALGEBRA “Circles” (9-6) A circle is a set of points that are the same distance from a given point called the center. What is a “circle”? How can you find the circumference of a circle? Note: Every circle has the same relationship between its circumference and diameter in which the ratio of its circumference to its diameter (circumference divided by diameter) is 22/7 or approximately 3.14. The symbol  known as “pi”, which is equal to 3.14, is a good estimate of this special ratio between a circle’s circumference (perimeter) and its diameter (distance across it) Since  is equal to, then by multiplying both sides of the equation by the diameter: C =  d, or C =  (2r), or C = 2  r What is a “radius”, “diameter”, “chord”, and “circumference”? circumference diameter

2. PRE-ALGEBRA Find the circumference of the circle. C = 2  r Write the formula. ≈ 37.68Simplify (wavy equal sign means “approximately”). The circumference of the circle is about 37.68 in. C = 2(3.14)(6) Replace  with 3.14 and r with 6. Circles LESSON 9-6 & 10-3 Additional Examples

3. PRE-ALGEBRA “Circles” (9-6) A central angle is an angle in which the vertex is the center of the circle. What is a “central angle”? Since there are 360 0 in a circle, you can find a central angle by creating a proportion in which the percent of the circle over 100 percent equals “x” (number of degrees) over 360 0. Example: In the figure below,  MON,  NOV,  VOA, and  AOM are central angles (NOTE: Point O is the vertex, or middle point, of all these angles,) How do you find a central angle? Example: Make a circle graph for Juan’s weekly budget shown in the table below.

4. PRE-ALGEBRA Make a circle graph for Jackie’s weekly budget. Jackie’s Weekly Budget Entertainment (e) Food (f) Transportation (t) Savings (s) 20% 10% 50% Use proportions to find the measures of the central angles. = = e = 72° t = 36° t 360 10 100 e 360 20 100 = f = 72° = s = 180° 50 100 s 360 f 360 20 100 Circles LESSON 9-6 Additional Examples

5. PRE-ALGEBRA Use a compass to draw a circle. Draw the central angles with a protractor. (continued) Add a title and necessary information. Jackie’s Weekly Budget Label each section. Savings Entertainment Food Transportation Circles LESSON 9-6 Additional Examples

6. PRE-ALGEBRA Draw a circle graph of the data. First add to find the total number of students. 120 + 82 + 137 + 101 = 440 p 67° s 83° Use proportions to find the measures of the central angles. f 98° j 112° = 137 440 j 360 = 101 440 s 360 = p 360 82 440 = 120 440 f 360 Spring Dance Attendance Freshmen (f) Sophomores (p) Juniors (j) Seniors (s) 120 82 137 101 Circles LESSON 9-6 Additional Examples

7. PRE-ALGEBRA (continued) Use a compass to draw a circle. Draw the central angles with a protractor. Seniors Freshmen Juniors Sophomores Label each section. Spring Dance Attendance Add a title and necessary information. Circles LESSON 9-6 Additional Examples