14 2 tangents to a circle lesson

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14 2 tangents to a circle lesson

  1. 1. Use Properties of Tangents 14-2
  2. 2. Vocabulary • Circle- the set of all pts in a plane that are equidistant from a given pt. called the center of the circle. • Radius- segment whose endpoints are the center and any point on the circle • Diameter- a chord that contains the center of the circle. • Two polygons are similar if corresponding angles are congruent and corresponding side lengths are proportional. ΔABC ∼ ΔDEF
  3. 3. P P is the center of the circle A B Segment AB is a diameter C Segments AP, PB, and PC are radii
  4. 4. Chord • Chord- a segment whose endpoints are on the circle. A B
  5. 5. Secant • Secant- a line that intersects a circle in 2 pts A B
  6. 6. Tangent • Tangent- a line in the plane of the circle that intersects the circle in exactly one point, called the point of tangency.
  7. 7. • Point of tangency- point where tangent intersects a circle TPoint T is the point of tangency
  8. 8. Example tell whether the segment is best described as a chord, secant, tangent, diameter or radius • Segment AH • Segment EI • Segment DF • Segment CE A B C D E F G H I
  9. 9. Example tell whether the segment is best described as a chord, secant, tangent, diameter or radius • Segment AH • Segment EI • Segment DF • Segment CE A B C D E F G H I tangent Diameter Chord radius
  10. 10. Tangent circles- circles that intersect in one point Concentric circles- circles that have a common center but different radii lengths
  11. 11. Common internal tangent- a tangent that intersects the segment that connects the centers of the circles Common external tangent- does not intersect the segment that connects centers
  12. 12. Example Common internal or external tangent?
  13. 13. Example Common internal or external tangent? external
  14. 14. Theorem 14-4 • In a plane, a line is tangent to a circle if and only if it is perpendicular to a radius of the circle at its endpoint on the circle.
  15. 15. Example Is segment CE tangent to circle D? Explain D E C 11 45 43 Remember in order to find if a line is tangent we need to know if there is a 90 degree angle
  16. 16. Example Is segment CE tangent to circle D? Explain D E C 11 45 43 112 +432 =452 121+1849=2025 1970=2050 NO Let’s use the Pythagorean Theorem
  17. 17. Example solve for the radius, r A B C r r 28ft 14ft
  18. 18. Example solve for the radius, r A B C r r 28ft 14ft r2 +282 =(r+14)2 r2 + 784=r2 + 28r+196 784=28r+196 588=28r 21=r
  19. 19. Theorem 14-6 • Tangent segments from a common external point are congruent.
  20. 20. Example segment AB is tangent to circle C at pt B. segment AD is tangent to circle C at pt D. Find the value of X C B D A x2 +8 44
  21. 21. Example segment AB is tangent to circle C at pt B. segment AD is tangent to circle C at pt D. Find the value of X C B D A x2 +8 44 x2 +8=44 x2 =36 X=6

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