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

Home > Shapes > Geometry
Special triangle in any triangle (Posted on 2002-11-05) Difficulty: 5 of 5
Prove or disprove, that the points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle. (In other words, that for any yellow triangle, the green triangle will be equilateral, given that the thinner lines trisect their respective angles.)

See The Solution Submitted by Dulanjana    
Rating: 4.0000 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts re(3): baa | Comment 10 of 20 |
(In reply to re(2): baa by LDoc)

by adding up all the central angles around/including the green triangle you will get (feel free to check me):

YXZ + ZYX + XZY + (AXY+AYX) + (BYZ+BZY) + (CZX+CXZ) + X + Y + Z =1080
sub in the given values for the combos

YXZ + ZYX + XZY + 180 - A/3 + 180 - B/3 + 180 - C/3 + (X + Y + Z) =1080
sub in from previous solution and combine like terms:

YXZ + ZYX + XZY - A/3 - B/3 - C/3 + 300=540
(YXZ + ZYX + XZY) - A/3 - B/3 - C/3 =240
sub in given

180 - A/3 - B/3 - C/3 =240
0= 60 + (A/3 + B/3 + C/3)
sub in found result

0= 60 + 120
0=180

the situation is not possible
  Posted by LDoc on 2002-11-07 18:07:28

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 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information