Posted by Bob on Tuesday, January 15, 2013 at 2:14pm.
Let the diagonals intersect at (0,0)
Then let the vertices of the kite be at
(-2a,0),(2a,0) and (0,2b),(0,-2c)
The midpoints of the sides are thus at
(a,b),(-a,b),(a,-c),(-a,-c)
Those are obviously the vertices of a rectangle.
Thanks :)