Expert: Paul Klarreich - 5/19/2007

Question
Some help, please :

Problem . Find the area,the radius of the inscribed circle and the radius of the circumscribed one for this triangle :

a= 12.7,  b = 21.5, and  c = 28.6

Answer
Questioner:   Kirk
Category:  Advanced Math
 
Subject:  Trigonometry
Question:  Some help, please :

Problem . Find the area,the radius of the incircle and the radius of the circumcircle for this triangle :

a= 12.7,  b = 21.5, and  c = 28.6
.........................................
Hi, Kirk,

There are a few formulas that are useful here:  (You can easily look them up under the terms:

1. Hero's Formula
2. Incircle or Inradius
3. Circumcircle or Circumradius


Let s = (a + b + c)/2, where a,b,c are as above.  This 's' is called the 'semiperimeter' because, it is, er....  half the perimeter.

************* VIEW IN COURIER FONT **********

Then:

1. The area of the triangle is: [Something called Hero's formula.]
         
A = sqrt(s(s - a)(s - b)(s - c))

2. The radius, r,  of the incircle is   A/s, where A is as above, so

         (s - a)(s - b)(s - c)
r = sqrt( --------------------- )
                  s

3. The radius, R, of the circumcircle is:

                    abc
R = --------------------------------------------  
   4 sqrt(s (a + b - s)(a + c - s)(b + c - s) )

So it will be a bit of calculator work (use Excel or something) but routine.

[Hmmm.... there does not seem to be any trigonometry here.]