chord
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The correct term for a line segment with both endpoints on a circle is a chord. The diameter of a circle is also a chord.
Some segments with both endpoints on a circle are not diameters.
Chord
A chord
No, it is not. A chord is a line segment. It cannot have a length of zero. A point has no dimensions. The chord of a circle is a line segment that has its endpoints (both of them) on the curve (or circumference) of the circle.