Label the Parts of the Circle

1. Label the Parts of the Circle • Center • Radius • Diameter • Minor Arc • Major Arc • Chord • Secant • Tangent

2. Circles Unit Essential Question: How does the intersection of lines and circles create specific arcs, lengths and angles?

3. 8-1 Tangent Lines Essential Question: What are the segment relationships when two intersecting lines pass through a circle?

4. Tangent

5. IF it’s not perpendicular • THEN create OL perpendicular to n. • BUT… • SO OP is perpendicular to n.

6. If the segments are Tangent,Then find x.

8. Converse of Theorem 12-1 • Is ML tangent?

9. Inscribed and Circumscribed

10. Find the Perimeter of each Triangle:

11. Find x to nearest Hundreth:

12. 8-2 Chords and Arcs Essential Question: What are the segment relationships when two intersecting lines pass through a circle?

13. Chord • A chord is a point whose endpoints are on a circle. • A secant is a line that intersects a circle in two points.

16. Chords Examples • Find a: Find x:

18. Find each missing length to nearest hundreth:

19. Example:

20. Exploring Inscribed Angles

21. 8-3 Inscribed Angles Essential Question: What are the angle relationships when two intersecting lines pass through a circle?

22. Inscribed Angles

23. Example: • Find a and b.

24. Corollaries:

25. Tough Example: • Find x and y.

26. Opener

27. 8-4 Angle Measures & Segment Lengths Essential Question: What are the angle relationships when two intersecting lines pass through a circle?

28. Chords and Secants • Secant – line intersecting circle at 2 points. • Chord – Segment with endpoints on the circle.

29. Inside: ADD Outside: SUBTRACT

30. Examples:

31. Segment Lengths:

32. Examples:

33. Wankel Engine