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

Home > Shapes > Geometry
Four Equal Triangles (Posted on 2013-06-16) Difficulty: 3 of 5

Here's a problem I found in the Problems section of a
math journal. The way I read it, it is not true.

Let ABCD be a convex quadrilateral. Prove that

there exists a point P inside ABCD such that
[PAB]=[PBC]=[PCD]=[PDA],

    if and only if

the diagonals bisect each other.

Here [XYZ] denotes the area of triangle XYZ.

See The Solution Submitted by Bractals    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Solution Comment 3 of 3 |
(In reply to re: Solution by Bractals)

Yes that would do it.  It is conceivable that the author of the problem had that in mind originally and someone thought they were neatening it up by changing it.

  Posted by Jer on 2013-06-17 15:13:56

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 (9)
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