### 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.

## 4 comments:

I guess GoldenRatio is a serious candidate

It's not immediately obvious that such points even exist, so this is a nice treat on many levels.

That hardly even looks like a rectangle.. I guess the triangle inside it is playing tricks on my eyes.

Hi! I posted this on my blog. Pat, I copied the picture off your blog, let me know if you don't want that.

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