THERE HAVE ALOT OF RELATIONSHIP
It'll be clearer if you are spefic by giving a sketch of what you mean.
1). if their angle of intersection is 90 degrees, then the arcs where sustended by the diameter of the circle
2). the angle of intersection of the segments is equal but opposite to the angle of the intersected arcs which is directly proportional to the lengths of the arcs.
3). If the intersection occurs at the centre of the circle, the length of the arc produced is a function of the radius of the circle.
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