Tangents Notes

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Tangents Notes

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Definition

• A tangent is a line that intersects a circle at
  exactly one point.
• The point at which
  a tangent intersects a
  circle is called the
  point of tangency.

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Factoid 1

• A line is tangent to a circle if and only if it
  is perpendicular to the radius drawn to the point
  of tangency.

radius
90 degrees perpendicular
tangent
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Factoid 2

• If two segments from the same exterior point are
  tangent to a circle, then they are congruent.

tangent 1
tangent 1
tangent 2
exterior point
tangent 2
They are congruent.
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Example
exterior point
Because of Factoid 2, x14.
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Example
Since a radius of the circle is 5, any radius is
5
Since it is a radius drawn to a point of
tangency, it is perpendicular to the tangent.
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a2 b2 c2 122 52 c2 144 25 c2 169
c2 13 c
?
This whole length is 13. x 5 13 x 8
5
12
ANSWER x 8
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Go to Work on Your Assignment

• There are 10 questions which are worth 10 points
  each.
• Show all work on your own paper.