Diagonals of a rhombus

Assume two points A and B are given. A rhombus ABDC is to be constructed by following point C to be freely chosen under the restriction that the segments AB(=f) and AC(=g) are equal. That is, C is a circumpoint of the circle with center A and radius f, and D is an intersection of a circle c with center C and radius f, and a line h through C and parallel to f.[br]Are the diagonals of this rhombus perpendicular?[br](This example was provided by Andreas Lindner.)[br][br][br][br][br]
Use the Relation tool to ask about relation between diagonals (k and l)

Information: Diagonals of a rhombus