perplexus.info :: Geometry : T-N-T

T-N-T (Posted on 2017-11-25)

Let ABC be an arbitrary triangle with points D, E, and F
lying on rays AB, BC, and CA respectively such that

   AD/AB = BE/BC = CF/CA = x.

Prove that Area(ΔDEF)/Area(ΔABC) = 3x² - 3x + 1.

See The Solution Submitted by Bractals

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re: Solution

Comment 2 of 2 |

(In reply to Solution by Jer)

Did you consider that x might be greater than 1 while working the problem? Base = (1-x)b would give a negative base. Also, triangle ABC would lie inside triangle DEF if x greater than 1.

Edited on November 28, 2017, 12:12 pm

Posted by Bractals on 2017-11-28 11:25:08

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