Expert: Paul Klarreich - 4/25/2007

Question

Pls derieve that the circum radius of equilateral trianle is side/sqrt(3) and inradius is side/(2*squr(3))

Answer
Questioner:   Pritesh
Category:  Advanced Math
 
Subject:  Circumradius Question
Question:  
Pls derieve that the circum radius of equilateral trianle is side/sqrt(3) and inradius is side/(2*squr(3))
............................................
Hi, Pritesh,

The following, derived from a recent answer to another questioner, should take care of both of these problems:
************ EXTRACT FROM ANSWER *******************
If there are no figures given, you make your own.  Draw the Eq. Tri.  Then construct the altitude from each vertex to the opposite side.  [ONLY ONE IS SHOWN.]  That's three of them and they meet at a point, call it C.  Now the distance from C to each of the sides is your radius. (THE INRADIUS) Your diagram will look like this:

USE COURIER FONT TO VIEW THIS.
       B
      /|\
     / | \
    /  |  \
   /   |   \
  /   C.    \
 /     |     \
/      |      \
E---------------A
       D

Also draw in CA on your paper.  Now you will find that:

Angle CAD = 30 degrees.
Angle CDA = 90
CD = r
AC = 2r (and so does BC)
[THAT'S YOUR CIRCUMRADIUS]

AD = r sqrt(3)