Angles and Tangents to a Circle

In the diagram, a tangent and a line drawn to the point of tangency form a right triangle. Solve for "?" (the length of the hypotenuse)

• 15

• 6

• -24

• 14

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CCSS.HSG.C.A.2

A point B is 17cm away from the centre O of a circle. AB is the tangent to the circle at A. Given that AB = 15 cm, find the radius of the circle.

• 8 cm

• 9 cm

• 2 cm

• 16 cm

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CCSS.HSG.C.A.2

What is the measure of ∠BDC?

• 64°

• 128°

• 32°

• 116°

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CCSS.HSG.C.A.2

Is line AB tangent to the circle? (Hint: all radii are the same length, and you have 2 radii there)

• YES

• No

• Can't be determined

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CCSS.HSG.C.A.2

Assume lines that look like tangents are tangents.

• 7.5

• 56.25

• 9.39

• 4.5

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CCSS.HSG.C.A.2

8.

• 67.5°

• 90°

• 22.5°

• 45°

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CCSS.HSG.C.A.2

The measure of arc GH is equal to

• 98

• 49

• 24.5

• 49π

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CCSS.HSG.C.A.2

The measure of arc XW is

• 45

  
  

  ^

• 90

• 135

• 67.5

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CCSS.HSG.C.A.2

The measure of arc XY is

• 54

  
  

  ^

• 180

• 216

• 74

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CCSS.HSG.C.A.2

Using the tangent lines, find the value of x. (Hint: the figure formed is a quadrilateral and you know the sum of the interior angles of a quadrilateral)

• 60

• 120

• 30

• 300

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CCSS.HSG.C.A.2