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

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.

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