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

Home > Just Math
CC & ET Expanded (Posted on 2018-12-29) Difficulty: 3 of 5

See the problem as posed originally here.

Triangle T has area A and sides of length a,b, and c.

Given 3 concentric circles of radius a,b,c, respectively, find the areas of the largest and smallest equilateral triangles with a vertex on each circle in terms of the given variables.

No Solution Yet Submitted by broll    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
solution | Comment 1 of 2
The smallest one is very easy as the minimum lengtht of the triangle with a vertex on each circle is c-a

Smallest: A=[(c-a)^2]/2. [Att: This is wrong[

Largest: It's difficult to find by oneself, but there is a formula for equilateral triangles

A= (1/2)*[(sqr3/4)*(a^2+b^2+c^2) + 3 Area T (abc)]
All this are known, so thats the solution

And I congratule for the one hundred number.... (to broll)

Edited on January 6, 2019, 11:21 am

Edited on January 12, 2019, 4:58 am
  Posted by armando on 2019-01-06 11:20:10

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