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Lesson 10.1

Lesson 10.1. Today, we are going to… > identify segments and lines related to circles > use properties of tangents to a circle. Parts of a Circle. C. Circle C. Diameter = _ radius . Y. N. BN. YX. AB. A. C. X. B. A chord is. Y. YX. AB. A. C. X. B. A secant is. AB.

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Lesson 10.1

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  1. Lesson 10.1 Today, we are going to… > identify segments and lines related to circles > use properties of tangents to a circle Parts of a Circle

  2. C Circle C Diameter = _ radius

  3. Y N BN YX AB A C X B A chord is

  4. Y YX AB A C X B A secant is

  5. AB XY X Y C B A A tangent is

  6. Common Tangent Lines internal tangents

  7. Common Tangent Lines external tangents

  8. Two circles can intersect in 2, 1, or 0 points. Draw 2 circles that have 2 points of intersection

  9. internally tangent circles Draw two circles that have 1 point of intersection

  10. externally tangent circles Draw two circles that have 1 point of intersection

  11. concentric circles Draw two circles that have no point of intersection

  12. 9. What are the center and radius of circle A? Center: Radius =

  13. 10. What are the center and radius of circle B? Center: Radius =

  14. 11. Identify the intersection of the two circles.

  15. 12. Identify all common tangents of the two circles.

  16. m Ð ABC = B C A

  17. B A C Theorem 10.1 & 10.2 A line is tangent to a circle if and only if it is _____________ to the radius from the point of tangency.

  18. 13. Find CA. C 7 D B 15 What is DA? A

  19. 14. Find x. C x 7 x x What is CA? B 8 6 16 15 A

  20. 15. Is AB a tangent? How do we test if 3 segments create a right triangle? C 10 7 26 B 6 24 15 A

  21. 16. Is AB a tangent? C 8 7 17 B 6 12 15 A

  22. Slope of AC? A C 17. Find the slope of line t. A (3,0) and C (5, -1) t Slope of line t?

  23. A B C A tangent segment One endpoint is the point of tangency.

  24. Theorem 10.3 If 2 segments from the same point outside a circle are tangent to the circle, then they are congruent.

  25. 18. Find x. B 7x - 2 A 3x + 8 C

  26. 19. Find x. B x2 + 25 A 50 C

  27. Lesson 10.2 Arcs and Chords Today, we are going to… > use properties of arcs and chords of circles

  28. C An angle whose vertex is the center of a circle is a central angle. A B

  29. Major Arc ADB C Minor Arc AB Minor Arc - Major Arc D A B

  30. D A 60˚ C B m AB = Measures of Arcs

  31. E D A B m AED = m ABD = m AD Semicircle C

  32. Find the measures of the arcs. 1. m BD 2. m DE 3. m FC 4. m BFD D C 68˚ 52˚ ? B 100˚ E 53˚ F

  33. E F D C A B AD and EB are diameters. 5. Find x, y, and z. x = x˚ 30˚ y = y˚ z = z˚

  34. Theorem 10.4 Two arcs are congruent if and only if their chords are congruent.

  35. 6. Find m AB B (3x + 11)° (2x + 48)° C A D

  36. Theorem 10.5 & 10.6 A chord is a diameter if and only if it is a perpendicular bisector of a chord and bisects its arc.

  37. 7. Is AB a diameter? A B

  38. 8. Is AB a diameter? A 8 8 B

  39. 9. Is AB a diameter? A B

  40. Theorem 10.7 Two chords are congruent if and only if they are equidistant from the center.

  41. B G A C D F E 10. Find CG. AB = 12 DE = 12 x 7 6 ?

  42. Lesson 10.3 Inscribed Angles Today, we are ALSO going to… > use properties of inscribed angles to solve problems

  43. An inscribed angle is an angle whose vertex is on the circle and whose sides contain chords of the circle.

  44. Theorem 10.8 If an angle is inscribed, then its measure is half the measure of its intercepted arc. 2x x

  45. x = 60° 1. Find x. 120° x°

  46. x = 140° 2. Find x. x° 70°

  47. Theorem 10.9 If 2 inscribed angles intercept the same arc, then the angles are congruent.

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