Definition
Chord
A chord is a straight line segment with both endpoints on a circle.
What it means
Pick any two points on the circle and join them with a ruler. The straight segment is a chord, even if it misses the center. The curved boundary between the same points is an arc, not the chord.
Remember it
A chord cuts straight across while an arc bends around.
Example
Points P and Q lie on a circle. Segment PQ is a chord. It does not pass through the center, so it is a chord but not a diameter.
Watch for
A segment from the center to one point on the circle is a radius, not a chord, because only one endpoint lies on the circle.
Common mix-up
Every diameter is a chord, but a chord that misses the center is not a diameter.
Exact meaning
A chord of a circle is a line segment whose two endpoints lie on the circle. A diameter is the special chord that passes through the circle’s center, and it is the longest chord of that circle.