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Triangle Properties, Common Tangents, and Inscribed Angles

This chapter covers properties of triangles, concentric circles, common tangents, and inscribed angles. It also includes exercises on circle equations and quadratic equations.

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Triangle Properties, Common Tangents, and Inscribed Angles

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  1. Chapter 11

  2. If 2 sides of a triangle are radii then the triangle is ______________

  3. isosceles .

  4. Coplanar circles with the same center are _________ circles

  5. concentric .

  6. A ________ arc is less than 180 0

  7. minor

  8. A diameter that is ______to a chord bisects that chord

  9. perpendicular .

  10. Create a right triangle: .

  11. .

  12. A line that is tangent to each of 2 coplanar circles is a __________

  13. common tangent

  14. How many common tangents do the following circles have? b. a. d. c.

  15. a. b. four three c. d. two one

  16. A radius is ________ to a tangent at the point of tangency

  17. perpendicular .

  18. Tangent segments from a point outside a circle are _________

  19. congruent A P PA = PB B

  20. The sides of an INSCRIBEDPOLYGON are _________ of a circle

  21. chords

  22. The vertex of a CENTRAL ANGLEis on the ______ and the sides contain _______

  23. center… radii .

  24. m 1 = ____ . 1 x 0

  25. m 1 = x o . 80o 80 o

  26. The vertex of an INSCRIBED ANGLE is on the ______ and thesides contain ________

  27. circle… chords .

  28. m 1= ______ . x o 1

  29. m 1= x __ 1 o 2 . o o 40 80

  30. m 1 = _______ 1 x o

  31. m 1 = x __ 1 o 2 o 100 o 200

  32. m 1 = _______ x o y 1 o

  33. m 1 = (x + y) 1 ___ 2 40 o o o 80 60

  34. m 1 = _____ yo 1 xo

  35. m 1 = (x - y)o 1 2 40o 20o 1000

  36. An angle inscribed in a semicircle is a _______ angle

  37. right .

  38. The opposite angles of an INSCRIBED QUADRILATERAL are _________________

  39. supplements 2 3 1 4 m 1 + m 3 = 180 m 2 + m 4 = 180

  40. Complete:( ___ )( ___ ) = ( ___ ) ( ___ ) d a c b

  41. ( a )( b ) = ( c )( d ) 3x = (4)(6) 3x = 24 x = 8 6 3 4 x

  42. b Complete:( ___ )( ___ ) = ( ___ )( ___ ) a c d

  43. (a)(a + b) = (c)(c + d) 7 5 (12) = 6 (6 + x) 60 = 36 + 6x 24 = 6x 4 = x 5 x 6

  44. Complete:( ___ )( ___ ) = ( ___ )2 b a c

  45. (a)(a + b) = (c)2 9 3(3 + 9) = x2 36 = x2 6 = x 3 x

  46. State the center and the radius of the following circle:(x – 4)2 + (y + 8)2 = 49

  47. (x – 4)2 + (y + 8)2 = 72Center (4, -8)Radius = 7

  48. Write the equation of a circle with center (-1, 3) and passing through (-4, -6)

  49. (x + 1)2 + (y – 3)2 = 90

  50. Given: 3x2 - 4x + 6a = _____b = _____c = _____

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