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Warm – up  Session 28
Math II Day 28 (9-17-09) UNIT QUESTION: What special properties are found with the parts of a circle? Standard:  MM2G1, MM...
AGENDA <ul><li>Notes 6.1 - Circles </li></ul><ul><li>Class Work </li></ul><ul><li>Home Work </li></ul>Friday 9/17 6.2
Chapter 6 Circles
Parts of a Circle Circle  – set of all points _________ from a given point called the _____  of the circle. C Symbol: equi...
CHORD: a segment whose ________ are on the circle endpoints
Radius P RADIUS: distance from the _____ to a point on the circle center
Diameter P DIAMETER: distance ______ the circle through its ______ center  across  Also known as the longest chord.
What is the relationship between the diameter and the radius of a circle? r  =  OR D  = ½ D 2 r
12 32 9 6 D = ? r = ?  r = ?  D = ? 24 16 4.5 12
Use   P to determine whether each statement is  true  or  false . P Q R T S
Secant Line A  secant line  intersects the circle at exactly TWO points. SECANT sounds like second
TANGENT:  a LINE that intersects the circle exactly ONE time
Point of Tangency
Name the term that best describes the line. Secant Radius Diameter Chord Tangent
Two circles can intersect… <ul><li>in two points </li></ul><ul><li>one point </li></ul><ul><li>or no points </li></ul>
No points of intersection (different center)
No points of intersection (same center) Concentric Circles Same center but different radii
1 point of intersection (Tangent Circles) Internally Tangent Externally Tangent
2 points of intersection
Common Tangents Internal
Common Tangents External
INTERIOR A point is  inside  a circle if its distance from the center is  less than  the radius. 
EXTERIOR A point is  outside  a circle if its distance from the center is  greater than  the radius. 
A point is  on  a circle if its distance from the center is  equal to  the radius. 
If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. ...
1.  Find x 9 x A B 12 a 2  + b 2  = c 2 x = 15 9 2  + 12 2  = x 2
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
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
R S T If two segments from the same exterior point are tangent to a circle, then they are congruent. Party hat problems!
R S T 4.  Find x
A C B 5.  Find x
A C E B D 6.  Find x. P
T S Q P N R 7.  Find NP
CW Workbook Page 199 #18-33
HW Page 186 #1-22
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6.1 circles---day-28-1

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Transcript of "6.1 circles---day-28-1"

  1. 1. Warm – up Session 28
  2. 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
  3. 3. AGENDA <ul><li>Notes 6.1 - Circles </li></ul><ul><li>Class Work </li></ul><ul><li>Home Work </li></ul>Friday 9/17 6.2
  4. 4. Chapter 6 Circles
  5. 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. 6. CHORD: a segment whose ________ are on the circle endpoints
  7. 7. Radius P RADIUS: distance from the _____ to a point on the circle center
  8. 8. Diameter P DIAMETER: distance ______ the circle through its ______ center across Also known as the longest chord.
  9. 9. What is the relationship between the diameter and the radius of a circle? r = OR D = ½ D 2 r
  10. 10. 12 32 9 6 D = ? r = ? r = ? D = ? 24 16 4.5 12
  11. 11. Use  P to determine whether each statement is true or false . P Q R T S
  12. 12. Secant Line A secant line intersects the circle at exactly TWO points. SECANT sounds like second
  13. 13. TANGENT: a LINE that intersects the circle exactly ONE time
  14. 14. Point of Tangency
  15. 15. Name the term that best describes the line. Secant Radius Diameter Chord Tangent
  16. 16. Two circles can intersect… <ul><li>in two points </li></ul><ul><li>one point </li></ul><ul><li>or no points </li></ul>
  17. 17. No points of intersection (different center)
  18. 18. No points of intersection (same center) Concentric Circles Same center but different radii
  19. 19. 1 point of intersection (Tangent Circles) Internally Tangent Externally Tangent
  20. 20. 2 points of intersection
  21. 21. Common Tangents Internal
  22. 22. Common Tangents External
  23. 23. INTERIOR A point is inside a circle if its distance from the center is less than the radius. 
  24. 24. EXTERIOR A point is outside a circle if its distance from the center is greater than the radius. 
  25. 25. A point is on a circle if its distance from the center is equal to the radius. 
  26. 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. 27. 1. Find x 9 x A B 12 a 2 + b 2 = c 2 x = 15 9 2 + 12 2 = x 2
  28. 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. 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. 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. 31. R S T 4. Find x
  32. 32. A C B 5. Find x
  33. 33. A C E B D 6. Find x. P
  34. 34. T S Q P N R 7. Find NP
  35. 35. CW Workbook Page 199 #18-33
  36. 36. HW Page 186 #1-22
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