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

Home > Shapes
Dodecagonal Diagonals (Posted on 2013-08-22) Difficulty: 3 of 5
Let ABCDEFGHIJKL be a regular 12-sided polygon. TRUE or FALSE: The diagonals AE, CF, and DH intersect in a point.

No Solution Yet Submitted by Danish Ahmed Khan    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution Comment 1 of 1
Each of the 12 angles is 10*180/12= 150

Call the possible point of crossing M

Consider triangles DEM and FEM.  If M really is a point then EM will be the same length in each.

Angles MED and MDE are both 45 so DEM is 90.  So EM is √2/2 times the side length.

Angle FME is 30 and MEF is 105 so FEM is 45.  Using the law of sines, EM is √2/2 times the side length.

So the answer is TRUE

  Posted by Jer on 2013-08-23 20:17:56
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 (4)
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