G.GCI.2 Angle Formed by 2 Chords

In the applet below, the gray angle is said to be an angle formed by 2 chords of a circle. Interact with this applet for a few minutes. As you do, be sure to change the locations of the BIG POINTS each time before re-sliding the slider! What are the relationships between the inscribed angles, arcs, and angles formed by intersecting chords?

Quick Demo: 0:48 sec - 1:33 sec (BGM: Edward Shearmur)