1. Circle Basics Central Angles
Circles, I
Circle Basics
Central Angles

2. Definition - Circle
A circle is the collection of all points in a plane equidistant from a given point called the center of the circle.

3. Definition - Circle
A circle is the collection of all points in a plane equidistant from a given point called the center of the circle. ⨀𝐶

4. Example – Identify the parts of a Circle
Name the circle
Name a radius of the circle
Name a chord of the circle
Name a diameter of the circle

5. Example – Identify the parts of a Circle
Name the circle
Name a radius of the circle
Name a chord of the circle
Name a diameter of the circle ⨀𝐾

6. Example – Identify the parts of a Circle
Name the circle
Name a radius of the circle
Name a chord of the circle
Name a diameter of the circle ⨀𝐾

7. Example – Identify the parts of a Circle
Name the circle
Name a radius of the circle
Name a chord of the circle
Name a diameter of the circle ⨀𝐾

8. Example – Identify the parts of a Circle
Name the circle
Name a radius of the circle
Name a chord of the circle
Name a diameter of the circle ⨀𝐾

9. Radius/Diameter
By the definition of a circle, the distance from the center to any point on the circle is always the same. Therefore, all radii are congruent (have the same measurement)
A diameter is the sum of 2 radii, thus,

10. Compute Radius and Diameter
Circle A has diameter 𝐷𝐹 , 𝑃𝐺 .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?

11. Compute Radius and Diameter
Circle A has diameter 𝐷𝐹 , 𝑃𝐺 .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?

12. Compute Radius and Diameter
Circle A has diameter 𝐷𝐹 , 𝑃𝐺 .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?

13. Compute Radius and Diameter
Circle A has diameter 𝐷𝐹 , 𝑃𝐺 .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?

14. Compute Radius and Diameter
Circle A has diameter 𝐷𝐹 , 𝑃𝐺 .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?

15. Compute Radius and Diameter
Circle A has diameter 𝐷𝐹 , 𝑃𝐺 .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?

16. Compute Radius and Diameter
Circle A has diameter 𝐷𝐹 , 𝑃𝐺 .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?

17. Compute Radius and Diameter
Circle A has diameter 𝐷𝐹 , 𝑃𝐺 .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?

18. Example 2 The diameter of circle A is 10, circle B 20 and circle C 14.
Find XB
Find BY

19. Definition – Circumference
The circumference of a circle is the distance around the circle. Essentially, the perimeter of a circle, denoted by C.

20. Definition – Circumference
The circumference of a circle is the distance around the circle. Essentially, the perimeter of a circle, denoted by C.
Find C if r = 7.
Find C if d = 12.5

21. Definition – Circumference
The circumference of a circle is the distance around the circle. Essentially, the perimeter of a circle, denoted by C.
Find C if r = 7.
Find C if d = 12.5

22. CW
Angles & Arcs

23. Definition – Central Angle
A central angle has the center of the circle as its vertex, and its sides contain two radii of the circle.

24. Example 1 – Central Angles
Compute the measurement of angle AOD in circle O.

25. Example 1 – Central Angles
Compute the measurement of angle AOD in circle O.

26. Example 1 – Central Angles
Compute the measurement of angle AOD in circle O.

27. Example 1 – Central Angles
Compute the measurement of angle AOD in circle O.

28. Example 1 – Central Angles
Compute the measurement of angle AOD in circle O.

29. Example 1 – Central Angles
Compute the measurement of angle AOD in circle O.

30. Example 1 – Central Angles
Compute the measurement of angle AOD in circle O.

31. CW 13, part 2