They are equidistant from the center of the circle
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They're congruent :)
Nothing special. You have two line segments with equal lengths. That's all.
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.