Circle
257. The Circle's Promise · A point's journey at a constant distance from a fixed centre
The distance from the centre O to the moving point P is always equal to the radius r.
A circle is the set of all points at a fixed distance — the radius r — from a fixed point, the centre O. As a point P travels around, OP stays equal to r, which is exactly what makes the curve a circle.
What this lesson covers
Try to break it
Drag P around the circle. The readout OP stays at exactly r at every position — that's the circle's definition. Try to push P off the circle and OP changes; the canvas snaps P back onto the boundary to keep OP = r.
How you build it
Draw a circle with centre O.
- Place the centre O of the circle.
- Draw a circle with a specific radius.
The proof, step by step
Prove that every point of the circle is the same distance r from the centre O.
- A circle is the locus of a point moving in a plane.
- The distance from a fixed point remains constant.
- The fixed point is the centre and the constant distance is the radius.
Worked example
A circle is the locus of a point moving in a plane such that its distance from a fixed point remains constant. If the fixed point is the centre and the constant distance is the radius, what is the largest chord of a circle called?
The largest chord of a circle is the diameter. It passes through the centre and its length is twice the radius.
- Circumference
- Diameter — correct
- Chord
- Radius