Tangent 2-12

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Tangents
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This photograph was taken 216 miles above Earth.
From this altitude, it is easy to see
the curvature of the horizon. Facts about circles
can help us understand details about Earth.
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circle all points that are the same distance from
the center of the circle. A circle with center C
is called circle C, or ?C.
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Definitions

• A radius is a line segment from the center to
  the circle.
• A diameter is a chord that passes through the
  center.

radius
center
diameter
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• The word radius (plural radii) is also used to
  denote the length of a radius
  
• The word diameter is also used to denote the
  length of a diameter
• Note that the diameter of a circle is twice its
  radius.

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• 1. If DE is a tangent line,
• What is the angle x?
• Because DE is a tangent line
• It must be perpendicular to the radius/diameter
  at the point of tangency.
• Angle D must be a right angle
• x 180 38 90 52

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• 2. If AB is tangent to circle C,
• Find the radius.
• Tangent is perpendicular
• Use Pythagorean Theorem
• C2 B2 A2
• (x8)2 122 x2
• x2 16x 64 144 x2
• 16x 80
• x 5

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• Is ML tangent to Circle N
• at L? Explain.
• If ML is tangent, than it will
• create a right angle at the
• point of tangency, and right triangle NLM
• We can use the Pythagorean theorem to check if it
  is a right triangle
• 72 242 252
• 49 576 625
• 625 625 , ?NLM is a right triangle
• ?L is 90 degrees
• LM is perpendicular to the radius at L, so
• LM is tangent to Circle N