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10.2 & 10.4 – Use Properties of Tangents And Use Inscribed Angles and Polygons

10.2 & 10.4 – Use Properties of Tangents And Use Inscribed Angles and Polygons. A. C. An angle whose vertex is the center of the circle. P. A. C. Arc of a circle that is less than 180 °. P. Two letters:. A. C. Arc of a circle that is more than 180 °. P. B. 3 letters:. A.

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10.2 & 10.4 – Use Properties of Tangents And Use Inscribed Angles and Polygons

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  1. 10.2 & 10.4 – Use Properties of Tangents And Use Inscribed Angles and Polygons

  2. A C An angle whose vertex is the center of the circle P

  3. A C Arc of a circle that is less than 180° P Two letters:

  4. A C Arc of a circle that is more than 180° P B 3 letters:

  5. A Arc of a circle that is 180° P B C 3 letters:

  6. Two circles with the same radius

  7. A B Arcs that have the same central angle C D

  8. The measure of a minor arc is the measure of its _____________ angle. central A x° C x° P

  9. 73° 73° 73° minor

  10. 73° 26° minor 26°

  11. 73° 154° minor 26°

  12. 107° 73° 206° major 26°

  13. 107° 73° 81° minor 26°

  14. 107° 73° 180° semicircle 26°

  15. 107° 73° 180° Semicircle 26°

  16. 107° 73° 287° major 26°

  17. 10.4 – Use Inscribed Angles and Polygons

  18. Inscribed angle: An angle whose vertex is on a circle and whose sides are chords of the circle

  19. Intercepted Arc: An arc that is inside an inscribed angle

  20. Inscribed Polygon : A polygon that has all of its vertices on a circle

  21. Circumscribed Circle: The circle that contains the vertices of a polygon

  22. half The measures of an inscribed angle is ________ the measure of its ______________ arc. intercepted AB 2 D = 2x° x°

  23. intercept If two inscribed angles of a circle _____________ the same arc, then the angles are _____________. congruent D  C

  24. A ________ triangle is inscribed in a circle iff the _______________ is a diameter of the circle. right hypotenuse B is a right angle because it inscribes a semicircle.

  25. quadrilateral A ____________________ can be inscribed in a circle iff its opposite angles are ______________. supplementary mD + mF = 180° mE + mG = 180°

  26. Find the indicated measure. 158 2 = = 79°

  27. Find the indicated measure. 180 2 = = 90° 90° 180°

  28. Find the indicated measure. = = 40  2 80°

  29. Find the indicated measure. 92 2 = = 46° 88° 92°

  30. Find the indicated measure. 80 2 = = 40° 100° 80°

  31. Find the indicated measure. 56 2 = = 28° 56°

  32. Find the measure of A and C. 80 2 mA = = 40° 64° 64 2 mC = = 32° 80°

  33. Find the measure of A and C. 146 2 mA = = 73° 146° 62 2 mC = = 31° 62°

  34. 68 2 = mPNO = 34°

  35. 62 2 = mQNP= 31° 62°

  36. = 62° 62°

  37. = 130° 62°

  38. = 112° 112° 62°

  39. = 248° 112° 62°

  40. Decide whether a circle can be circumscribed about the figure. No, 70 + 130  180

  41. Decide whether a circle can be circumscribed about the figure. Yes, 91 + 89 = 180 91°

  42. Decide whether a circle can be circumscribed about the figure. No, 115 + 63  180

  43. Find the value of the variables. 5x + 110 = 180 2y + 104 = 180 5x = 70 2y = 76 x = 14° y = 38°

  44. Find the value of the variables. x + 108 = 180 y + y = 180 x = 72° 2y = 180 y = 90°

  45. Find the value of the variables. 44° 4x = 84+44 2 7y = 152+44 2 1 1 14y = 196 8x = 128 y = 14° x = 16°

  46. Find the value of the variables. 171° 12x = 96+48 2 3y = 48+171 2 1 1 6y = 219 24x = 144 y = 36.5° x = 6°

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