Problem (Circumcircles and Kites)

 

Tools: Anything you know (except what you are proving).

Let ABCD be a kite (with |AB| = |AD| and |CB| = |CD|). Which of the following is true?

  1. For any kite ABCD, there is a circle that passes through A, B, C and D.
  2. For no kites ABCD, there is a circle that passes through A, B, C and D.
  3. For some kites ABCD, there is a circle that passes through A, B, C and D.

 

If (I) or (ii) is true, justify your answer. If (iii) is true, describe all the kites for which there is such a circle and justify your answer.