perplexus.info :: Geometry : Squaring sides

Squaring sides (Posted on 2005-05-04)

Take any convex quadrilateral ABCD, with diagonals AC and BD. Pick E so ABCE is a parallelogram. Prove that AB²+BC²+CD²+DA²= AC²+BD²+DE².

Given the same quadrilateral, let P and Q be the midpoints of AC and BD. Now prove that AB²+BC²+CD²+DA²= AC²+BD²+4PQ².

Submitted by Federico Kereki

Rating: 4.0000 (2 votes)

Solution: (Hide)

These problems were solved by Euler, and you can find the answers here.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: The analytic geometry way (part 1 only)	nikki	2005-05-06 12:31:16
The analytic geometry way (part 1 only)	Jer	2005-05-05 17:42:01
re: 2nd proof w/ a cheat	Amon	2005-05-05 00:36:33
2nd proof w/ a cheat	nikki	2005-05-04 19:54:38

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info