The line connecting the points is called a chord; the part of the perimeter of the circle enclosed is called an arc; the area between an arc and the chord is called a circular segment.
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It would be call the ARC.
A segment between two points on a circle is
The two points and the centre of the earth define a plane, and the intersection of this plane with the surface of the earth is a circle - the "Great Circle". The shortest distance between the two points is the smaller of the two arcs on this circle.
well its true that every chord contains two points of the circumference of a circle 'cos a chord is the straight line between two points on the circumference
It is a chord of which the circle's diameter is the largest.