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

Home > Shapes > Geometry
Triangle Circle (Posted on 2004-11-20) Difficulty: 3 of 5
Begin with a right triangle with hypotenuse h.

Inscribe a circle and label its radius, r.

What is the ratio of the area of the circle to that of the triangle?

See The Solution Submitted by SilverKnight    
Rating: 3.0000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution r in terms of a, b, h | Comment 6 of 8 |

Formula for r as a function of the sides of the triangle:
Picture the triangle plus the point at the center of the circle.  Draw 3 lines from the center of the circle, one to each vertex.  Now the triangle is divided into 3 smaller triangles and like ancient Gaul, the 3 parts add up to the whole.

(1/2)ab = (1/2)ra + (1/2)rb + (1/2)rh
ab= r*(a+b+h)
r= ab/(a+b+h)

From np_rt, Ratio = Pi*r/(r+h)
so

Ratio= Pi*a*b/(ab+ah+bh+h^2)

for an isosceles right triangle, this = .5390 (the maximum)
for a 3,4,5 triangle it is = .5236
for a 30-60-90 triangle it is = .4860


  Posted by Larry on 2004-11-20 20:38:17
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 (3)
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