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

Home > Shapes > Geometry
Length of Angle Bisector (Posted on 2010-11-07) Difficulty: 3 of 5
In the below diagram, various segment lengths in rectangle ABCD have been marked and segment EG bisects angle DEF. What is the length of segment EG?

See The Solution Submitted by Charlie    
Rating: 2.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 3

|ED| = 17 = |EF|  and
angle DEG = angle FEG. Therefore,
Triangles DEG and FEG are congruent.
Thus, |DG| = |FG|. Therefore,
  20^2 + |AG|^2 = |DA|^2 + |AG|^2
                = |DG|^2 = |FG|^2
                = |GB|^2 + |BF|^2
                = |GB|^2 + 5^2
                or
  |GB|^2 - |AG|^2 = 20^2 - 5^2
                or
  (|GB| - |AG|)(|GB| + |AG|)
  = (|GB| - |AG|)(25) =  (20 - 5)(25)
Thus,
  |GB| - |AG| = 15
  |GB| + |AG| = 25
Therefore, |AG| = 5. Thus,
  |EG| = sqrt(|DA|^2 + [|DE| - |AG|]^2)
       = sqrt(20^2 + 12^2) 
       = sqrt(544) ~= 23.3238

 

  Posted by Bractals on 2010-11-07 14:15:50
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 (14)
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