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

Given a circumference of radius r=10 cm and a point p, what position does the point p have if its distance from the center of the circumference is:

  1. 9 cm
  2. 10 cm
  3. 11 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. as the distance from the center to the point is smaller than the diameter the point is interior to circumference.
  2. as the distance from the center to the point is equal to the diameter the point is on the circumference.
  3. as the distance from the center to the point is greater than the diameter the point is outside the circumference.

Solution:

  1. interior
  2. on the circumference
  3. exterior
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