1. 9.1 – 9.2 Exploring Circles
Geometry

2. Objectives/Assignment
Find the circumference of a circle
Use circumference to solve other problems

3. Definitions
Circle – is the set of all points in a plane that are equidistance from a given point on that plane
Center- “The given“ point on the plane
Radius- A segment that has one endpoint at the center of a circle and the other end point on the circle itself

4. Definitions Chord – A segment that has both endpoint on a circle
Diameter - Is a chord that contains the center of the circle.
Circumference - The distance around the circle

5. Finding circumference
The circumference of a circle is the distance around the circle.
For all circles, the ratio of the circumference to the diameter is the same.
This ratio is known as  or pi.

6. Circumference of a Circle
The circumference C of a circle is C = d or C = 2r, where d is the diameter of the circle and r is the radius of the circle.

7. Example #1

8. Example # 2
Find
a. the circumference of a circle with radius 6 centimeters
b. the radius of a circle with circumference 31 meters.

9. Solution: C = 2r = 2 •  • 6 = 12  37.70b. a.
C = 2r
= 2 •  • 6
= 12
 37.70
So, the circumference is about cm.
C = 2r
31 = 2r
31 = r
4.93  r
So, the radius is about 4.93 cm. 2

10. Practice

11. Take Notes

12. Take Notes
C = 2 *3.14* 7 = 44
D = 2 * r = 14
C = 2 *3.14* 16.2 = 101.8
R = D / 2 = 16.2

13. Take Notes
116.5 = 2 * 3.14 * r
116.5 = 6.28 * r
R = 18.6
D = 2 * r = 18.6 * 2 = 37.1

14. Take Notes
C = 2 * 3.14 * 12
C = 6.28 * 12
C = 75.4
D = 2 * r = 2* 12 = 24

15. Take Notes D² = 5² + 5² D² = 10² + 24² D² = 25 +25 C = 2 * 3.14 * 14

16. And… Sum Of Central Angles

20. Practice

21. 4x + 35 = 9x +5
30 = 5x
X = 6
AE = = 4 * = 59
ED = = 9 * = 59
ے 1 + ے 2 + ے 3 = 180 , = 62
ے 3 = ے 4 ( vertical) = 62
ے 1 + ے 3 = = 121
ے 4 + ے 2 = = 121

22. 360 - ے 1 + ے 2 + ے 3 + ے4 ,
= 118 =
= 118
ے 1 + ے 2 + ے 3 + ے4 = 242
DC =ے 3 = 62
ے 1 + ے 2 + ے 3 = 180