Tangent Properties

1
Tangent Properties

• Recall that a tangent to a circle touches the
  circle at a single point
• The rails on train tracks are tangent to the
  wheels of a train
• Tangent circles are two circles that are tangent
  to the same line
• Two circles are internally tangent if one circle
  is inside the other circle
• Two circles are externally tangent if neither
  circle is inside the other

2
Tangent Properties

• Investigation 1
• Tangent to a Circle
• Step 1 Construct a large circle and label the
  center O.
• Step 2 Using your straightedge, draw a line
  that appears to touch the circle at only one
  point. Label the point T.
• Step 3 Construct radius OT, and use a
  protractor to measure both angles at T.
• Step 4 Complete the conjecture below.
• C-59 Tangent Conjecture
• A tangent to a circle is perpendicular to the
  radius drawn to the point of tangency

3
Tangent Properties

• Investigation 2
• Tangent Segments
• Step 1 Construct a circle and label the center
  E.
• Step 2 Choose a point outside the circle and
  label it N.
• Step 3 Draw two lines passing through point N
  that are tangent to circle E.
• Step 4 Label the points of tangency A and G.
• Step 5 Compare the length of the tangent
  segments NA and NG, and complete the conjecture
  below.
• C-60 Tangent Segments Conjecture
• Tangent segments to a circle from a point
  outside the circle are congruent