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s diameter of the circle in the drawing above is the segment
The diameter is the distance across the circle. So if you split the circle in half by drawing a line through it, the diameter would be the length of that line.
This is simply the pitch circle diameter multiplied by cosine of pressure angle, which is most commonly 20 degrees.
It does the same thing that the height of a person does . . . it provides a way to describe the circle to other people without drawing a picture.
The cord of a circle that contains the center of that circle is a diameter of that circle.