1. Warm – up Session 28

2. Math II Day 28 (9-17-09) UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MM2G1, MM2G2 Today’s Question: What are the parts of a circle? Standard: MM2G3.a,d

4. Chapter 6 Circles

5. Parts of a Circle Circle – set of all points _________ from a given point called the _____ of the circle. C Symbol: equidistant center C

6. CHORD: a segment whose ________ are on the circle endpoints

7. Radius P RADIUS: distance from the _____ to a point on the circle center

8. Diameter P DIAMETER: distance ______ the circle through its ______ center across Also known as the longest chord.

9. What is the relationship between the diameter and the radius of a circle? r = OR D = ½ D 2 r

10. 12 32 9 6 D = ? r = ? r = ? D = ? 24 16 4.5 12

11. Use  P to determine whether each statement is true or false . P Q R T S

12. Secant Line A secant line intersects the circle at exactly TWO points. SECANT sounds like second

13. TANGENT: a LINE that intersects the circle exactly ONE time

14. Point of Tangency

15. Name the term that best describes the line. Secant Radius Diameter Chord Tangent

17. No points of intersection (different center)

18. No points of intersection (same center) Concentric Circles Same center but different radii

19. 1 point of intersection (Tangent Circles) Internally Tangent Externally Tangent

20. 2 points of intersection

21. Common Tangents Internal

22. Common Tangents External

23. INTERIOR A point is inside a circle if its distance from the center is less than the radius. 

24. EXTERIOR A point is outside a circle if its distance from the center is greater than the radius. 

25. A point is on a circle if its distance from the center is equal to the radius. 

26. If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. Point of Tangency More Pythagorean Theorem type problems! Yeah!! 

27. 1. Find x 9 x A B 12 a 2 + b 2 = c 2 x = 15 9 2 + 12 2 = x 2

28. 2. Find RQ a 2 + b 2 = c 2 8 P R 12 Q RQ = 16 12 2 + (QR) 2 = (8+12) 2 12 2 + (QR) 2 = 20 2

29. 3. Find the radius. r 2 + 24 2 = (r + 16) 2 16 A B 24 C r = 10 r 2 + 576 = r 2 + 32r + 256 320 = 32r

30. R S T If two segments from the same exterior point are tangent to a circle, then they are congruent. Party hat problems!

31. R S T 4. Find x

32. A C B 5. Find x

33. A C E B D 6. Find x. P

34. T S Q P N R 7. Find NP

35. CW Workbook Page 199 #18-33

36. HW Page 186 #1-22