Nothing special. You have two line segments with equal lengths. That's all.
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They are equidistant from the center of the circle
They're congruent :)
They are arcs of congruent circles.
If they're in the same circle or in circles of equal radii (radiuses), then yes.
If two chords intersect within a circle, the product of the two segments of one chord equals the product of the two segments of the other chord. In short, if two chords intersect in a circle, their length is equal.