prove that --

the diagonals of a rhombus intersect each other at 90 degrees.

suppose,

 ABCD is the rhombus and a circle is drawn with AB as diameter.

 let P be the point of intersection of the diagonals.

now,angle APB=90 degrees.

so

any circle with AB as diameter must pass thru Pp(since the angle in a semi circle is always 90 degrees)