From: rusin@vesuvius.math.niu.edu (Dave Rusin)
Newsgroups: sci.math
Subject: Re: A couple of probably basic questions...
Date: 10 Jul 1996 05:26:08 GMT

In article <4r0dvf$62c@gerry.cc.keele.ac.uk>,
P.H. Johnson <ged08@cc.keele.ac.uk> wrote:
>Q1. I have 3 triangles and I need to know the dimensions of the largest
>sphere (diameter or volume) that could fit through each.
>
>The triangle dimensions are as follows:
>
>		Side 1		Side 2		Side 3
>Triangle 1	112		109		108
>Triangle 2	96		92		113
>Triangle 3	112		116		110

If I understand correctly you seek the diameter of the (largest possible)
inscribe circle in these triangles. I hope I'm remembering correctly
when I give this formula: if the sides are  a, b, and  c, let
s = (a+b+c)/2; then the radius of the inscribed triangle is
	sqrt((s-a)(s-b)(s-c)/s)
and of course the diameter is twice that. 

For example, Triangle  1  gives a diameter of about  63.268.

dave