On Jan 5, 8:29 pm, Avni Pllana <avni...@hotmail.com> wrote: > Let ABCD be an arbitrary rectangle. Let DEFG be a rectangle such that E is an arbitrary point on the line through AB, and FG passes through C. If S1 is the area of ABCD, determine the area S2 of DEFG. > > Best regards, > Avni
Tilting of rigid rectangle DABC to position DEFG by an angular rotation t about fulcrum D creates four similar triangles. If DAE = angle t, the new sides so obtained DE and to DG are respectively multiplied and divided by the same sec(t), making the product area constant.
Best Regards, Narasimham
PS: ( Quite lateral to this post ! ) I wonder if the area of these two rectangles would still remain constant in hyperbolic geometry with two circular arc sides,when viewed as inversions about an arbitrary circle centered at fulcrum D.