Problems from A line in the plane: positions regarding a circumference

Given a circumference of radius $$r = 15$$ cm and a line $$r$$, what position does that line have if its distance from the center of the circumference is:

  1. $$0$$ cm
  2. $$1$$ cm
  3. $$14$$ cm
  4. $$15$$ cm
  5. $$17$$ cm
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Development:

Note: to resolve this exercise, it is very fortuitous to take paper and pencil and draw a picture of each case to see the solution clearly.

  1. the distance from the center to the line is less than the radius, so it is a secant line.

  2. the distance from the center to the line is less than the radius, so it is a secant line.

  3. the distance from the center to the line is less than the radius, so it is a secant line.

  4. the distance from the center to the line is equal to the radius, so it is a tangent.

  5. the distance from the center to the line is greater than the radio, so it is an external line.

Solution:

  1. secant
  2. secant
  3. secant
  4. tangent
  5. external
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