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Part of 2009 Oral Moscow Geometry Olympiad

Problems(2)

conctruct line to a parallelogram such that folded you can create a rhombus

Source: 2009 Oral Moscow Geometry Olympiad grades 8-9 p1

The figure shows a parallelogram and the point

P

of intersection of its diagonals is marked. Draw a straight line through

P

so that it breaks the parallelogram into two parts, from which you can fold a rhombus. https://1.bp.blogspot.com/-Df2tIBthcmI/X2ZwIx3R4vI/AAAAAAAAMhQ/8Zkxfq30H8MSCdc66tm33n6jt-QKfGMowCLcBGAsYHQ/s0/2009%2Boral%2Bmoscow%2Bj1.png

geometryparallelogramrhombusConstruct

smaller sides but larger diagonals of 2 quadrilaterals

Source: 2009 Oral Moscow Geometry Olympiad grades 10-11 p1

Are there two such quadrangles that the sides of the first are less than the corresponding sides of the second, and the corresponding diagonals are larger?
(Arseniy Akopyan)

geometrysidelengthsdiagonals