Circles
43. The Circle's Secret · One center, one distance, endless points
The distance from the center to the moving point is always the radius.
A circle is the set of all points in a plane that are at the same fixed distance (the radius) from a fixed point (the centre O). Drag the moving point — its distance from O always equals the radius.
What this lesson covers
Try to break it
Grab point P and try to pull it off the circle. Can you make the distance OP anything other than the radius? You can't — a circle is the set of all points at that exact fixed distance from the center. That's the definition!
How you build it
Draw a circle with a given radius.
- Mark the centre point O.
- With the circle tool, draw a circle with centre O — every point on it is the same distance (the radius) from O.
The proof, step by step
Prove that every point of the circle is the same distance from the centre O.
- The center O is fixed.
- The distance OP is constant.
- P traces the circumference.
Worked example
A circle is defined as the path traced by a moving point that always remains at a fixed distance from a fixed point. What is this fixed distance called?
The fixed distance from the center to any point on the circumference is called the radius.
- Radius — correct
- Diameter
- Chord
- Secant