Skyline 5.4 Part 2B (circumscribed angle)

You can imagine a triangle circumscribed around circle A. To help hone in the relationship between a circumscribed angle and the arcs they intersect we are just displaying one vertex of the triangle. Points B and C are draggable.
Drag the points/lines around and observe the arcs and the angle formed at the intersection of the two lines.[br]What relationship can you identify between the angle and the arcs?

Information: Skyline 5.4 Part 2B (circumscribed angle)