Congruent Chords Action (A)

In the applet below, two congruent chords will be drawn in the same circle. Interact with this applet for a few minutes, then answer the questions that follow. Feel free to adjust the lengths of these chords using the blue slider. Also, be sure to change the locations of the pink points each time after resetting the slider!
Questions: 1) Based upon your observations, what can you conclude about any 2 congruent chords drawn in the same circle? 2) Prove this fact true using the format of a 2-column or paragraph proof.

Quick Demo: 1:28 sec to 1:52 sec (BGM: Andy Hunter)