1. Geometry 10-6
Circles and Arcs

2. Words 2 Know Circle- all points equidistant from a given point
Center- middle of the circle
Radius- segment with endpoints at the center and a point of the circle.

3. More Words 2 Know
Congruent Circles- If the radii are congruent than the circles are congruent.
Diameter- a chord that contains the center
Central Angle- angle with the vertex at the center.

4. Find angle of each .30∗360=108° .20∗360=72° .08∗360=28.8°
.22∗360=79.2°
.07∗360=25.2°
.05∗360=18°

5. Even More Words 2 Know Semicircle- The arc of a half circle
Major Arc- Arc that is greater than a semicircle
Minor Arc- Arc that is less than a semicircle
Semicircle- 𝑋𝐴𝑍
Major Arc- 𝑋𝐷𝐴
Minor Arc- 𝑋𝐴

6. Major and Minor Arcs
Major
𝐴𝐵𝐹
𝐴𝐹𝐷
𝐸𝐵𝐹
Minor 𝐴𝐵 𝐸𝐵 𝐸𝐹
And more

7. Arc Addition Postulate
The measure of the arc formed by two adjacent arcs is the sum of the measure of the two arcs.
𝑚 𝐴𝐵𝐷 =𝑚 𝐴𝐵 +𝑚 𝐵𝐷

8. 𝐵𝐸 𝑖𝑠 𝑡ℎ𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 find…𝐴𝐸
80° 𝐷𝐸
120°
𝐴𝐸𝐷
200°
𝐷𝐴𝐸
240°

9. Even More Words 2 Know Circumference- The distance around a circle
Concentric Circles- Two circles with the same center.
Arc Length- A fraction of a circle
Congruent Arcs- Arcs with the same measure and on the same circle or a congruent circle.

10. Circumference
To find the circumference of a circle you use the formula:
𝐶=𝜋2𝑟 𝑜𝑟 𝐶=𝜋𝑑

11. Find the Circumference
Red:
90𝜋 𝑚 2
Orange:
100𝜋 𝑚 2

12. Arc Length
𝐴𝐿= 𝑚 𝐴𝐵 360 ∗2𝜋𝑟

13. 𝐴𝐿= 𝑚 𝐴𝐵 360 ∗2𝜋𝑟
∗2𝜋(3)
5 12 ∗6𝜋
30𝜋 12
2.5𝜋 𝑢𝑛𝑖𝑡𝑠

14. Show Your Work
Find 𝐴𝐵

15. Page 569 #2-38 even Show Your Work
Homework
Page 569 #2-38 even Show Your Work

16. Calvin and Hobbes
By: Bill Watterson