2. Aim: What are properties of a Circle? Course: Applied Geo. In the figure above, two parallel lines are cut by a transversal. If the m  6 = 2x – 4 and m  3x + 44, find m  4. Aim: What are some interesting points about a circle?! Do Now: 1 3 4 5 6 7 8 2 What’s the relationship between  6 &  1? 2x – 4 + 3x + 44 = 180 5x + 40 = 180 5x = 140 x = 28 1. m  4 = m  1 - vertical  s Evaluate 3x + 44, if x = 28: 2. m  4 & m  6 are supplementary - Interior  s on same side of transversal 3(28) + 44 = 128 0 = m  4 supplementary

3. Aim: What are properties of a Circle? Course: Applied Geo. Aim: What are some interesting points about a circle?! Do Now: Why 

4. Aim: What are properties of a Circle? Course: Applied Geo. The Circle

5. Aim: What are properties of a Circle? Course: Applied Geo. A circle is the set of all points in a plane equidistant from a given point called the center. Introducing the Circle

6. Aim: What are properties of a Circle? Course: Applied Geo. A Radius - a segment with one endpoint at the center and the other endpoint on the circle. Ex. OA B C Diameter - a segment that contains the center and has both endpoints on the circle. Example BC O Anatomy of Circle

7. Aim: What are properties of a Circle? Course: Applied Geo. OA B C The Radius of a circle is 1/2 the length of the Diameter The Diameter is twice the length of the Radius. The Center is the midpoint of any Diameter. Center, Diameter, Radius Relationships

8. Aim: What are properties of a Circle? Course: Applied Geo. OA Chord - Segments with endpoints on the circle DE D E B C Arc - a part of a circle ex. AC Anatomy of Circle - II

9. Aim: What are properties of a Circle? Course: Applied Geo.  is the ratio of the circumference of any circle to its diameter. The circumference is approximately 3.14 (22/7) times bigger than the diameter. O B C Circumference Circumference - the “perimeter” of a circle - the distance of one complete revolution C D 1d1d 2d2d3d3d.14d C =  D =  2r Circumference & Pie (π)

10. Aim: What are properties of a Circle? Course: Applied Geo. Find the circumference of a circle, to the nearest tenth, if the diameter is 14. C =  D =  2R C = 3.14(14) = 43.96  44.0 C =  (14) = 14  C = (22/7)(14) = 44 Find the radius of a circle, to the nearest tenth, if the circumference is 63. 63 = 3.14(2R ) 20.063694 = (2R) 10.031847 = R  10.0 Model Problems

11. Aim: What are properties of a Circle? Course: Applied Geo. A manufacturer advertises that a new car has a turning radius of only 16.1 ft. The distance between the two front tires is 4.7 ft. How much farther must the outer wheel travel in making a complete circle than the tires on the inside? Model Problem 16.1 ft. 11.4 ft. Radius of inner circle? 16.1 ft. - 4.7 ft. = 11.4 ft. C =  D =  2R C O = π(2)(16.1) C O = π(32.2) C I = π(2)(11.4) C I = π(22.8) C O - C I = 32.2  22.8   ft. 4.7 ft.

12. Aim: What are properties of a Circle? Course: Applied Geo. The diameter of a bicycle wheel is 26 in. To the nearest whole number, how many revolutions does the wheel make when the bicycle travels 100 yards. 1. Find the circumference of the wheel C = π D = π 2R C = π26 = 3.14(26) = 81.64 in. 26” 100 yds. 2. Find how many inches in 100 yds. 36 x 100 = 3600 inches 3. Divide inches traveled by circumference 3600  81.64 = 44.096031  44 revolutions Model Problem

13. Aim: What are properties of a Circle? Course: Applied Geo. The Product Rule

14. Aim: What are properties of a Circle? Course: Applied Geo. The Product Rule

15. Aim: What are properties of a Circle? Course: Applied Geo. The Product Rule