Question

When segments intersect inside a circle, what is the relationship between the angle of intersection and the intercepted arcs? @jigglypuff314

Answer 1

I'm not sure if this is what you're looking for?
When two chords intersect each other inside a circle, the products of their segments are equal.
http://www.mathopenref.com/chordsintersecting.html

Answer 2

The measure of the angle formed by two chords which intersect inside the circle is 1/2 the sum of the intercepted arcs.