### Recently reminded of this pretty idea...

Came across a geometry problem with an interesting result which I did not suspect... thought I would share...

In the figure, rectangle ABCD is inscribed with a triangle by selecting points E and F on the segments AB and BC respectively, so that triangles AED, BEF, and CFD all have equal area. Find the ratios of AE:EB and BF:FC. I was surprised, and pleased, hope you are as well.