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Rhombus in Rectangle

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.

Center Path

Stage: 3 and 4 Challenge Level: Challenge Level:1
Four rods of equal length are hinged at their endpoints to form a rhombus ABCD. The diagonals AC and BD meet at X.

AB is kept fixed and CD is allowed to move in the plane.

Describe the locus of the point X and prove your assertion.

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