10.3 Tangents in a CircleMath 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 PropertiesThe radius is perpendicular to the tangent at the point of tangency.

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

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

8

8

8

60

60

60

30

30

1. Using the diagram to the right, determine:a) AD = 16 b) ABD = ∠ 90 c) ACB = ∠ 120 d) AB = 13.9 e) AE = •

8

8

8

60

60

60

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 = ∠ 60 d) AB = 13.9 e) AE = 18.9•

8

8

8

60

60

60

AE2 = 102 + 162

AE2 = 100 + 256

AE2 = 356

AE =

2. Determine the length x:

x2 = 142 + 62

x2 = 196 + 36

x2 = 232

x =

3. Determine the length x:

d2 + 52 = 132

d2 + 25 = 169

d2 = 144

d =

X = = 6 cm

d

Θ = 180 – (90 + 50) = 180 – 140 = 40

50

90

45

20Θ = 180 – (45 + 20) = 180 – 65 = 115

• 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.

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

EC2 = 82 + 62

EC2 = 64+ 36

EC2 = 100

EC = 8

6

Practice

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