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

Home > Shapes > Geometry
Incentroid (Posted on 2019-02-24) Difficulty: 3 of 5
The segment formed by joining the incenter and centroid of a certain right triangle is parallel to one of its legs and has a length of 1 unit.

Find the perimeter of this triangle.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Comment 2 of 2 |

Let AHB be the right triangle with a, h, and b 
the lengths of sides HB, BA, and AH
respectively ( h^2 = a^2 + b^2 ). Let I denote
the incenter and M the centroid. We will
assume that b > a. Let r denote the inradius
with r = ( a + b - h ) / 2.

IM parallel to AH ==> a/3 = r 
                         ==> a = 3b/4 & h = 5b/4

|IM| = b/3 - r     ==> |IM| = b/12

Perimeter = ( a + b + h ) / |IM|
                  = ( 3b/4 + b + 5b/4 ) / b/12
                  = 36 

Edited on March 4, 2019, 11:51 pm
  Posted by Bractals on 2019-03-04 23:47:55

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 (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information