Congruent Chords (I)

Interact with the following applet below for a few minutes, then answer the questions that follow. Be sure to change the locations of the BIG POINTS each time before re-sliding the slider!
Questions: 1) Explain why the 2 circles shown are congruent. How do you know? 2) Notice how there are 3 congruent chords displayed. The red arc is said to be the arc "determined" (or "made") by these chords. Complete the following statement by filling in the blanks to make a true statement: In the same circle or _________________________ circles, _________________ chords determine ________________________ arcs. 3) Write a formal, 2-column proof of this statement.

Quick Demo: 0:58 sec to 1:28 sec (BGM: Andy Hunter)