All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
T-N-T (Posted on 2017-11-25) Difficulty: 3 of 5

  
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    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Question 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

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information