perplexus.info :: Geometry : Variation on a Classic

Variation on a Classic (Posted on 2005-08-23)

In the classic problem you are given a triangle ABC with points D on AB, E on BC, and F on AC such that |AD|=2|DB|, |BE|=2|EC|, and |CF|=2|FA|. The lines AE, BF, and CD enclose a triangle inside triangle ABC. You are to find the area of this enclosed triangle relative to that of ABC. The answer is 1/7.

What if everything is the same except |BE|=|EC| and |CF|=3|FA|. What is the area of the enclosed triangle relative to that of ABC?

See The Solution Submitted by McWorter

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Subject	Author	Date
Puzzle Answer	K Sengupta	2022-08-24 21:56:54
re(3): Independent solution?	Bractals	2005-08-25 08:12:01
re(2): Independent solution?	McWorter	2005-08-24 23:36:32
re: Independent solution?	Bractals	2005-08-24 22:38:48
Independent solution?	McWorter	2005-08-24 16:25:12
Solution	Bractals	2005-08-24 04:26:42
re(3): According to Geometer's Sketchpad... (spoiler)	McWorter	2005-08-23 20:28:19
re(2): According to Geometer's Sketchpad... (spoiler)	Charlie	2005-08-23 20:22:30
re: According to Geometer's Sketchpad... (spoiler)	McWorter	2005-08-23 20:20:32
re(2): According to Geometer's Sketchpad... (spoiler)	Charlie	2005-08-23 20:19:18
re(2): According to Geometer's Sketchpad... (spoiler)	McWorter	2005-08-23 20:11:35
re: According to Geometer's Sketchpad... (spoiler)	Charlie	2005-08-23 18:42:00
According to Geometer's Sketchpad... (spoiler)	Charlie	2005-08-23 18:24:42

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