Question

When segments intersect outside a circle, what is the relationship between the angle of intersection and the intercepted arcs

Answer 1

are they tangents to the circle, or what

Answer 2

depends.. here are some cases to look at
http://www.regentsprep.org/Regents/math/geometry/GP15/CircleAngles.htm

Answer 3

usually you see, it is half of the difference in the larger and smaller arc angles formed from the lines

Answer 4

The vertex of the angle is on the circle. That makes the angle an inscribed angle. It is equal to 1/2 the intercepted arc.