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

Home > Shapes > Geometry
Two Center Distance (Posted on 2010-09-18) Difficulty: 3 of 5
The center of a circle having radius 1 is denoted by O. The triangle ABC is inscribed within the circle such that the respective areas of the circular segments described by the sides AB, BC and AC are in the ratio 3:4:5.

A circle with its center located at P is inscribed within the triangle.

Determine the distance OP.

No Solution Yet Submitted by K Sengupta    
Rating: 2.5000 (2 votes)

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

I'm going to take my life in my hands and guess 0.2:

For the ratios of the circular segments to be so nearly the same, the triangle must very nearly be equilateral. If we take the middle side to be approximately 1.7, the required condition is satisfied if the other sides are approximately 1.6 and 1.8. Now, the product of the incircle radius and circumcircle radius of a triangle with sides a,b,c is (a*b*c)/(2(a+b+c)) = .48, while the distance, d, between the circumcentre and the incentre is: d^2 = R(R-2r) ; here d^2 = 1(1-.96), so d = 0.2

I won't be surprised to be proved wrong!

 


  Posted by broll on 2010-09-19 12:25:56
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 (2)
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