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10.3 Tangents in a Circle

10.3 Tangents in a Circle. Math 9. A tangent is a line that touches the circle at one point. The point where the tangent touches the circle is called the point of tangency What appears to be the size of the angle between the tangent and the radius ? 90 . Tangent Properties.

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10.3 Tangents in a Circle

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  1. 10.3 Tangents in a Circle Math 9

  2. A tangent is a line that touches the circle at one point. The point where the tangent touches the circle is called the point of tangency What appears to be the size of the angle between the tangent and the radius? 90

  3. Tangent Properties The radius is perpendicular to the tangent at the point of tangency.

  4. A chord drawn perpendicular to a tangent at the point of tangency passes through the center of the circle, and is thus a diameter

  5. 1. Using the diagram to the right, determine: a) AD = 16 b) ∠ABD = 90 c) ∠ACB =120 d) AB = e) AE = 8 60 30 60 8 60 8 30

  6. AB2 + 82 = 162 AB2 + 64 = 256 AB2= 192 AB = 1. Using the diagram to the right, determine: a) AD = 16 b) ∠ABD = 90 c) ∠ACB =120 d) AB = 13.9 e) AE = 8 60 60 8 60 8

  7. AE2 = 102 + 162 AE2 = 100 + 256 AE2= 356 AE = 1. Using the diagram to the right, determine: a) AD = 16 b) ∠ABD = 90 c) ∠ACB =60 d) AB = 13.9 e) AE = 18.9 8 60 60 8 60 8

  8. 2. Determine the length x: x2 = 142 + 62 x2 = 196 + 36 x2= 232 x =

  9. d2 + 52 = 132 d2+ 25 = 169 d2= 144 d = X = = 6 cm 3.Determine the length x: d

  10. Θ = 180 – (90 + 50) = 180 – 140 = 40 90 50

  11. Θ = 180 – (45 + 20) = 180 – 65 = 115 20 45

  12. 6. A wireless router is located at point C and produces a strong signal for distances up to 24 m. How much closer does a computer at point A have to be moved towards point C so that it can receive the signal? AC2 = 182 + 242 AC2 = 324+ 576 AC2= 900 AC = 30-24 = 6 The router needs to be moved 6 meters closer.

  13. 7. Determine the value of x and the size of ∠ADB. ∠ABD = 90 3x + 3 + 2x + 7 = 90 5x + 10 = 90 -10 -10 5x = 80 ÷5 ÷5 x = 16 ∠ADB = 2x + 7 = 2(16) + 7 = 32 + 7 = 39

  14. EC2= 82+ 62 EC2= 64+ 36 EC2= 100 EC = 6 8

  15. Practice p. 399 3, 5, 7, 9, 10, 14, 17

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