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 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