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10.1– Use Properties of Tangents

10.1– Use Properties of Tangents. The set of all points in a plane that are equidistant from a given point. Point equidistant from the sides of the circle. Gives the name of the circle. P. A segment with endpoints at the center and on the circle. Q. P. Q. A.

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10.1– Use Properties of Tangents

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  1. 10.1– Use Properties of Tangents

  2. The set of all points in a plane that are equidistant from a given point

  3. Point equidistant from the sides of the circle. Gives the name of the circle. P

  4. A segment with endpoints at the center and on the circle Q P

  5. Q A A segment with both endpoints on the circle P

  6. A segment with both endpoints on the circle that goes through the center of the circle Q P R

  7. Q A line that intersects a circle in two points. P R

  8. A line that intersects a circle in exactly one point. P Q R

  9. The point where a tangent line touches a circle P Q S R S

  10. A line that is tangent inside two circles.

  11. A line that is tangent outside two circles.

  12. Two circles on the same plane

  13. Circles that have the same center

  14. tangent In a plane, a line is ______________ to a circle if and only if the line is ____________________ to a radius of the circle and its endpoint on the circle. perpendicular

  15. Tangent segments from a common ____________ point are ___________________. external congruent C A B

  16. 1. State the best term for the given figure. C center

  17. 1. State the best term for the given figure. Common internal tangent

  18. 1. State the best term for the given figure. radius

  19. 1. State the best term for the given figure. chord

  20. 1. State the best term for the given figure. Point of Tangency

  21. 1. State the best term for the given figure. diameter

  22. 1. State the best term for the given figure. secant

  23. 1. State the best term for the given figure. Common External Tangent

  24. 2. Find the radius of 2u

  25. 3. Find the diameter of 4u

  26. 4. Find the center of (2, 4)

  27. 5. The points K and M are points of tangency. Find the value of x. x = 22

  28. 5. The points K and M are points of tangency. Find the value of x. 4x + 7 = 7x – 8 7 = 3x – 8 15 = 3x 5 = x

  29. 6. In the diagram, is a radius of Determine whether is tangent to Explain your reasoning. c2 = a2 + b2 52 = 32 + 42 25 = 9 + 16 25 = 25 Right Triangle Yes

  30. 6. In the diagram, is a radius of Determine whether is tangent to Explain your reasoning. c2 = a2 + b2 192 = 82 + 162 361 = 64 + 256 361 > 320 Not a Right Triangle NO

  31. 7. Given the picture, find the indicated length. c2 = a2 + b2 802 = a2 + 482 6400 = a2 + 2304 4096 = a2

  32. Given the picture, find the indicated length. c2 = a2 + b2 252 = x2 + 122 6 625 = x2 + 144 481 = x2

  33. Given the picture, find the indicated length. Given the picture, find the indicated length. c2 = a2 + b2 (r + 2)2 = r2 + 42 (r + 2)(r + 2) = r2 + 16 r2 + 2r + 2r + 4 = r2 + 16 r2 + 4r + 4 = r2 + 16 4r + 4 = 16 4r = 12 r = 3

  34. Given the picture, find the indicated length. c2 = a2 + b2 (r + 9)2 = r2 + 152 (r + 9)(r + 9) = r2 + 225 r2 + 9r + 9r + 81 = r2 + 225 r2 + 18r + 81 = r2 + 225 18r + 81 = 225 18r = 144 r = 8

  35. HW Problem #21 c2 = a2 + b2 (r + 16)2 = r2 + 242 (r + 16)(r + 16) = r2 + 576 r2 + 16r + 16r + 256 = r2 + 576 r2 + 32r + 256 = r2 + 576 32r + 256 = 576 32r = 320 r = 10

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